#vectors — Public Fediverse posts

Alright, future engineers!
**Dot Product:** A scalar measure of how much two vectors point in the same direction.
Ex: For `v=[v1,v2], w=[w1,w2]`, `v.w = v1w1 + v2w2`.
Pro-Tip: If `v.w = 0`, they're orthogonal (perpendicular)! Great for checking vector alignment.
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar measure of how much two vectors point in the same direction.
Ex: For `v=[v1,v2], w=[w1,w2]`, `v.w = v1w1 + v2w2`.
Pro-Tip: If `v.w = 0`, they're orthogonal (perpendicular)! Great for checking vector alignment.
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar measure of how much two vectors point in the same direction.
Ex: For `v=[v1,v2], w=[w1,w2]`, `v.w = v1w1 + v2w2`.
Pro-Tip: If `v.w = 0`, they're orthogonal (perpendicular)! Great for checking vector alignment.
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar measure of how much two vectors point in the same direction.
Ex: For `v=[v1,v2], w=[w1,w2]`, `v.w = v1w1 + v2w2`.
Pro-Tip: If `v.w = 0`, they're orthogonal (perpendicular)! Great for checking vector alignment.
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar measure of how much two vectors point in the same direction.
Ex: For `v=[v1,v2], w=[w1,w2]`, `v.w = v1w1 + v2w2`.
Pro-Tip: If `v.w = 0`, they're orthogonal (perpendicular)! Great for checking vector alignment.
#LinearAlgebra #Vectors #STEM #StudyNotes

Cat containment - from roaming to staying at home

"Cats are a popular pet in Australia: second only to dogs, they’re found in a third of homes, with about 5.3 million felines nationally."

"Keeping cats indoors can keep them safe from harm and protect native wildlife. But how can pet owners support their furry friends in making the transition?"

"When cats catch bird flu, the virus can be deadly. One study, published by the American Veterinary Medical Association, found domestic cats infected with H5N1 had overall mortality rates of 50 to 70%."

"Keeping pets indoors, contained in outdoor enclosures known as “catios”, or on a harness, also protects native wildlife. Each roaming puss kills about 186 mammals, reptiles and birds every year, according to research by the Threatened Species Recovery Hub."

“A safe cat is an indoor cat,” says wildlife veterinarian Dr Tania Bishop. “Roaming cats already face threats from cars, snakes, dogs, ticks, powerful owls and disease. With H5 bird flu now at our doorstep, there is also a risk cats could become infected by scavenging or coming into contact with sick or dead birds.”

“Cat containment is one of those rare measures that’s a win for everyone – it’s better for cats, better for wildlife and better for communities.” >>
https://www.theguardian.com/australia-news/2026/aug/08/how-to-keep-outdoor-cat-indoors-protect-environment
#pets #cats #roaming #vectors #CatContainment #disease #ticks #BirdFlu #wildlife #biodiversity

Image: Poster of one of the many missing roaming cats of #Bellingen

Cat containment - from roaming to staying at home

"Cats are a popular pet in Australia: second only to dogs, they’re found in a third of homes, with about 5.3 million felines nationally."

"Keeping cats indoors can keep them safe from harm and protect native wildlife. But how can pet owners support their furry friends in making the transition?"

"When cats catch bird flu, the virus can be deadly. One study, published by the American Veterinary Medical Association, found domestic cats infected with H5N1 had overall mortality rates of 50 to 70%."

"Keeping pets indoors, contained in outdoor enclosures known as “catios”, or on a harness, also protects native wildlife. Each roaming puss kills about 186 mammals, reptiles and birds every year, according to research by the Threatened Species Recovery Hub."

“A safe cat is an indoor cat,” says wildlife veterinarian Dr Tania Bishop. “Roaming cats already face threats from cars, snakes, dogs, ticks, powerful owls and disease. With H5 bird flu now at our doorstep, there is also a risk cats could become infected by scavenging or coming into contact with sick or dead birds.”

“Cat containment is one of those rare measures that’s a win for everyone – it’s better for cats, better for wildlife and better for communities.” >>
https://www.theguardian.com/australia-news/2026/aug/08/how-to-keep-outdoor-cat-indoors-protect-environment
#pets #cats #roaming #vectors #CatContainment #disease #ticks #BirdFlu #wildlife #biodiversity

Image: Poster of one of the many missing roaming cats of #Bellingen

Cat containment - from roaming to staying at home

"Cats are a popular pet in Australia: second only to dogs, they’re found in a third of homes, with about 5.3 million felines nationally."

"Keeping cats indoors can keep them safe from harm and protect native wildlife. But how can pet owners support their furry friends in making the transition?"

"When cats catch bird flu, the virus can be deadly. One study, published by the American Veterinary Medical Association, found domestic cats infected with H5N1 had overall mortality rates of 50 to 70%."

"Keeping pets indoors, contained in outdoor enclosures known as “catios”, or on a harness, also protects native wildlife. Each roaming puss kills about 186 mammals, reptiles and birds every year, according to research by the Threatened Species Recovery Hub."

“A safe cat is an indoor cat,” says wildlife veterinarian Dr Tania Bishop. “Roaming cats already face threats from cars, snakes, dogs, ticks, powerful owls and disease. With H5 bird flu now at our doorstep, there is also a risk cats could become infected by scavenging or coming into contact with sick or dead birds.”

“Cat containment is one of those rare measures that’s a win for everyone – it’s better for cats, better for wildlife and better for communities.” >>
https://www.theguardian.com/australia-news/2026/aug/08/how-to-keep-outdoor-cat-indoors-protect-environment
#pets #cats #roaming #vectors #CatContainment #disease #ticks #BirdFlu #wildlife #biodiversity

Image: Poster of one of the many missing roaming cats of #Bellingen

Cat containment - from roaming to staying at home

"Cats are a popular pet in Australia: second only to dogs, they’re found in a third of homes, with about 5.3 million felines nationally."

"Keeping cats indoors can keep them safe from harm and protect native wildlife. But how can pet owners support their furry friends in making the transition?"

"When cats catch bird flu, the virus can be deadly. One study, published by the American Veterinary Medical Association, found domestic cats infected with H5N1 had overall mortality rates of 50 to 70%."

"Keeping pets indoors, contained in outdoor enclosures known as “catios”, or on a harness, also protects native wildlife. Each roaming puss kills about 186 mammals, reptiles and birds every year, according to research by the Threatened Species Recovery Hub."

“A safe cat is an indoor cat,” says wildlife veterinarian Dr Tania Bishop. “Roaming cats already face threats from cars, snakes, dogs, ticks, powerful owls and disease. With H5 bird flu now at our doorstep, there is also a risk cats could become infected by scavenging or coming into contact with sick or dead birds.”

“Cat containment is one of those rare measures that’s a win for everyone – it’s better for cats, better for wildlife and better for communities.” >>
https://www.theguardian.com/australia-news/2026/aug/08/how-to-keep-outdoor-cat-indoors-protect-environment
#pets #cats #roaming #vectors #CatContainment #disease #ticks #BirdFlu #wildlife #biodiversity

Image: Poster of one of the many missing roaming cats of #Bellingen

Cat containment - from roaming to staying at home

"Cats are a popular pet in Australia: second only to dogs, they’re found in a third of homes, with about 5.3 million felines nationally."

"Keeping cats indoors can keep them safe from harm and protect native wildlife. But how can pet owners support their furry friends in making the transition?"

"When cats catch bird flu, the virus can be deadly. One study, published by the American Veterinary Medical Association, found domestic cats infected with H5N1 had overall mortality rates of 50 to 70%."

"Keeping pets indoors, contained in outdoor enclosures known as “catios”, or on a harness, also protects native wildlife. Each roaming puss kills about 186 mammals, reptiles and birds every year, according to research by the Threatened Species Recovery Hub."

“A safe cat is an indoor cat,” says wildlife veterinarian Dr Tania Bishop. “Roaming cats already face threats from cars, snakes, dogs, ticks, powerful owls and disease. With H5 bird flu now at our doorstep, there is also a risk cats could become infected by scavenging or coming into contact with sick or dead birds.”

“Cat containment is one of those rare measures that’s a win for everyone – it’s better for cats, better for wildlife and better for communities.” >>
https://www.theguardian.com/australia-news/2026/aug/08/how-to-keep-outdoor-cat-indoors-protect-environment
#pets #cats #roaming #vectors #CatContainment #disease #ticks #BirdFlu #wildlife #biodiversity

Image: Poster of one of the many missing roaming cats of #Bellingen

Female #antalates can serve as #vectors for introducing #phoreticorganisms, such as #mites, from an established #colony into a newly founded #nest. Hitching a ride on a #youngqueen can be a key #dispersalstrategy for #myrmecophilous #phoreticmites.
However, some #phoretic species also utilize other routes, such as via #workerants.
© #StefanFWirth

Support my work: https://ko-fi.com/sfwirth

Reading:
H. Klompen & K. U. Campbell (2024)
https://doi.org/10.1007/s00040-024-01003-z

#Photos:
©S. F. Wirth, L. niger #queen

Female #antalates can serve as #vectors for introducing #phoreticorganisms, such as #mites, from an established #colony into a newly founded #nest. Hitching a ride on a #youngqueen can be a key #dispersalstrategy for #myrmecophilous #phoreticmites.
However, some #phoretic species also utilize other routes, such as via #workerants.
© #StefanFWirth

Support my work: https://ko-fi.com/sfwirth

Reading:
H. Klompen & K. U. Campbell (2024)
https://doi.org/10.1007/s00040-024-01003-z

#Photos:
©S. F. Wirth, L. niger #queen

Female #antalates can serve as #vectors for introducing #phoreticorganisms, such as #mites, from an established #colony into a newly founded #nest. Hitching a ride on a #youngqueen can be a key #dispersalstrategy for #myrmecophilous #phoreticmites.
However, some #phoretic species also utilize other routes, such as via #workerants.
© #StefanFWirth

Support my work: https://ko-fi.com/sfwirth

Reading:
H. Klompen & K. U. Campbell (2024)
https://doi.org/10.1007/s00040-024-01003-z

#Photos:
©S. F. Wirth, L. niger #queen

Female #antalates can serve as #vectors for introducing #phoreticorganisms, such as #mites, from an established #colony into a newly founded #nest. Hitching a ride on a #youngqueen can be a key #dispersalstrategy for #myrmecophilous #phoreticmites.
However, some #phoretic species also utilize other routes, such as via #workerants.
© #StefanFWirth

Support my work: https://ko-fi.com/sfwirth

Reading:
H. Klompen & K. U. Campbell (2024)
https://doi.org/10.1007/s00040-024-01003-z

#Photos:
©S. F. Wirth, L. niger #queen

Female #antalates can serve as #vectors for introducing #phoreticorganisms, such as #mites, from an established #colony into a newly founded #nest. Hitching a ride on a #youngqueen can be a key #dispersalstrategy for #myrmecophilous #phoreticmites.
However, some #phoretic species also utilize other routes, such as via #workerants.
© #StefanFWirth

Support my work: https://ko-fi.com/sfwirth

Reading:
H. Klompen & K. U. Campbell (2024)
https://doi.org/10.1007/s00040-024-01003-z

#Photos:
©S. F. Wirth, L. niger #queen

All of the little guys together.

#art #digitalart #illustration #graphicdesign #texture #vectors #cute #animals #scotland

All of the little guys together.

#art #digitalart #illustration #graphicdesign #texture #vectors #cute #animals #scotland

All of the little guys together.

#art #digitalart #illustration #graphicdesign #texture #vectors #cute #animals #scotland

All of the little guys together.

#art #digitalart #illustration #graphicdesign #texture #vectors #cute #animals #scotland

All of the little guys together.

#art #digitalart #illustration #graphicdesign #texture #vectors #cute #animals #scotland

Here's the final two Scottish Mammals illustrations done with textures.

Plus both are also now on my INPRNT store as well: https://www.inprnt.com/gallery/clasticartistic/

#art #graphicdesign #vectors #animals #cute #digitalart #fediart

Here's the final two Scottish Mammals illustrations done with textures.

Plus both are also now on my INPRNT store as well: https://www.inprnt.com/gallery/clasticartistic/

#art #graphicdesign #vectors #animals #cute #digitalart #fediart

Here's the final two Scottish Mammals illustrations done with textures.

Plus both are also now on my INPRNT store as well: https://www.inprnt.com/gallery/clasticartistic/

#art #graphicdesign #vectors #animals #cute #digitalart #fediart

Here's the final two Scottish Mammals illustrations done with textures.

Plus both are also now on my INPRNT store as well: https://www.inprnt.com/gallery/clasticartistic/

#art #graphicdesign #vectors #animals #cute #digitalart #fediart

Here's the final two Scottish Mammals illustrations done with textures.

Plus both are also now on my INPRNT store as well: https://www.inprnt.com/gallery/clasticartistic/

#art #graphicdesign #vectors #animals #cute #digitalart #fediart

Engineers!
**Dot Product:** Measures how much two vectors point in the same direction, yielding a scalar.
Ex: `[a,b] . [c,d] = ac + bd`.
Pro-Tip: If `v.w = 0`, vectors `v` and `w` are perpendicular. Key for orthogonality checks!
#LinearAlgebra #Vectors #STEM #StudyNotes

Engineers!
**Dot Product:** Measures how much two vectors point in the same direction, yielding a scalar.
Ex: `[a,b] . [c,d] = ac + bd`.
Pro-Tip: If `v.w = 0`, vectors `v` and `w` are perpendicular. Key for orthogonality checks!
#LinearAlgebra #Vectors #STEM #StudyNotes

Engineers!
**Dot Product:** Measures how much two vectors point in the same direction, yielding a scalar.
Ex: `[a,b] . [c,d] = ac + bd`.
Pro-Tip: If `v.w = 0`, vectors `v` and `w` are perpendicular. Key for orthogonality checks!
#LinearAlgebra #Vectors #STEM #StudyNotes

Engineers!
**Dot Product:** Measures how much two vectors point in the same direction, yielding a scalar.
Ex: `[a,b] . [c,d] = ac + bd`.
Pro-Tip: If `v.w = 0`, vectors `v` and `w` are perpendicular. Key for orthogonality checks!
#LinearAlgebra #Vectors #STEM #StudyNotes

Engineers!
**Dot Product:** Measures how much two vectors point in the same direction, yielding a scalar.
Ex: `[a,b] . [c,d] = ac + bd`.
Pro-Tip: If `v.w = 0`, vectors `v` and `w` are perpendicular. Key for orthogonality checks!
#LinearAlgebra #Vectors #STEM #StudyNotes

All intro physics textbooks show students how to decompose a vector into components along orthonormal axes. If you know if a textbook that shows how to decompose a vector into components along non-orthonormal axes (e.g. the sides of a parallelogram), please give me the reference. #ITeachPhysics #Vectors

All intro physics textbooks show students how to decompose a vector into components along orthonormal axes. If you know if a textbook that shows how to decompose a vector into components along non-orthonormal axes (e.g. the sides of a parallelogram), please give me the reference. #ITeachPhysics #Vectors

All intro physics textbooks show students how to decompose a vector into components along orthonormal axes. If you know if a textbook that shows how to decompose a vector into components along non-orthonormal axes (e.g. the sides of a parallelogram), please give me the reference. #ITeachPhysics #Vectors

All intro physics textbooks show students how to decompose a vector into components along orthonormal axes. If you know if a textbook that shows how to decompose a vector into components along non-orthonormal axes (e.g. the sides of a parallelogram), please give me the reference. #ITeachPhysics #Vectors

Alright, future engineers!
**Linear Transformation:** A function that maps vectors, preserving addition & scalar mult.
Ex: `T(v) = Av` (matrix A transforms vector v).
Pro-Tip: It 'stretches', 'rotates', or 'reflects' space. Visualize it!
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Linear Transformation:** A function that maps vectors, preserving addition & scalar mult.
Ex: `T(v) = Av` (matrix A transforms vector v).
Pro-Tip: It 'stretches', 'rotates', or 'reflects' space. Visualize it!
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Linear Transformation:** A function that maps vectors, preserving addition & scalar mult.
Ex: `T(v) = Av` (matrix A transforms vector v).
Pro-Tip: It 'stretches', 'rotates', or 'reflects' space. Visualize it!
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Linear Transformation:** A function that maps vectors, preserving addition & scalar mult.
Ex: `T(v) = Av` (matrix A transforms vector v).
Pro-Tip: It 'stretches', 'rotates', or 'reflects' space. Visualize it!
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Linear Transformation:** A function that maps vectors, preserving addition & scalar mult.
Ex: `T(v) = Av` (matrix A transforms vector v).
Pro-Tip: It 'stretches', 'rotates', or 'reflects' space. Visualize it!
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Linear Independence:** Vectors are LI if no vector can be written as a combination of the others.
Ex: `c1*v1 + c2*v2 = 0` implies `c1=c2=0`.
Pro-Tip: LI vectors form the building blocks (basis) of a vector space. No redundancy!
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Linear Independence:** Vectors are LI if no vector can be written as a combination of the others.
Ex: `c1*v1 + c2*v2 = 0` implies `c1=c2=0`.
Pro-Tip: LI vectors form the building blocks (basis) of a vector space. No redundancy!
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Linear Independence:** Vectors are LI if no vector can be written as a combination of the others.
Ex: `c1*v1 + c2*v2 = 0` implies `c1=c2=0`.
Pro-Tip: LI vectors form the building blocks (basis) of a vector space. No redundancy!
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Linear Independence:** Vectors are LI if no vector can be written as a combination of the others.
Ex: `c1*v1 + c2*v2 = 0` implies `c1=c2=0`.
Pro-Tip: LI vectors form the building blocks (basis) of a vector space. No redundancy!
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Linear Independence:** Vectors are LI if no vector can be written as a combination of the others.
Ex: `c1*v1 + c2*v2 = 0` implies `c1=c2=0`.
Pro-Tip: LI vectors form the building blocks (basis) of a vector space. No redundancy!
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar showing how much two vectors point in the same direction.
Ex: `u . v = u1v1 + u2v2`
Pro-Tip: If `u . v = 0`, vectors are orthogonal (perpendicular)! Super useful for geometry & projections.
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar showing how much two vectors point in the same direction.
Ex: `u . v = u1v1 + u2v2`
Pro-Tip: If `u . v = 0`, vectors are orthogonal (perpendicular)! Super useful for geometry & projections.
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar showing how much two vectors point in the same direction.
Ex: `u . v = u1v1 + u2v2`
Pro-Tip: If `u . v = 0`, vectors are orthogonal (perpendicular)! Super useful for geometry & projections.
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar showing how much two vectors point in the same direction.
Ex: `u . v = u1v1 + u2v2`
Pro-Tip: If `u . v = 0`, vectors are orthogonal (perpendicular)! Super useful for geometry & projections.
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar showing how much two vectors point in the same direction.
Ex: `u . v = u1v1 + u2v2`
Pro-Tip: If `u . v = 0`, vectors are orthogonal (perpendicular)! Super useful for geometry & projections.
#LinearAlgebra #Vectors #STEM #StudyNotes

**Linear Independence:** Vectors are independent if none can be formed by scaling & adding the others.
Ex: `[1,0]` and `[0,1]` are independent.
Pro-Tip: If the only solution to `c1v1 + c2v2 = 0` is `c1=c2=0`, your vectors are independent!
#LinearAlgebra #Vectors #STEM #StudyNotes

**Linear Independence:** Vectors are independent if none can be formed by scaling & adding the others.
Ex: `[1,0]` and `[0,1]` are independent.
Pro-Tip: If the only solution to `c1v1 + c2v2 = 0` is `c1=c2=0`, your vectors are independent!
#LinearAlgebra #Vectors #STEM #StudyNotes

**Linear Independence:** Vectors are independent if none can be formed by scaling & adding the others.
Ex: `[1,0]` and `[0,1]` are independent.
Pro-Tip: If the only solution to `c1v1 + c2v2 = 0` is `c1=c2=0`, your vectors are independent!
#LinearAlgebra #Vectors #STEM #StudyNotes

**Linear Independence:** Vectors are independent if none can be formed by scaling & adding the others.
Ex: `[1,0]` and `[0,1]` are independent.
Pro-Tip: If the only solution to `c1v1 + c2v2 = 0` is `c1=c2=0`, your vectors are independent!
#LinearAlgebra #Vectors #STEM #StudyNotes

**Linear Independence:** Vectors are independent if none can be formed by scaling & adding the others.
Ex: `[1,0]` and `[0,1]` are independent.
Pro-Tip: If the only solution to `c1v1 + c2v2 = 0` is `c1=c2=0`, your vectors are independent!
#LinearAlgebra #Vectors #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar value representing how much two vectors point in the same direction.
Ex: `[a,b] . [c,d] = ac + bd`
Pro-Tip: If the dot product is zero, the vectors are orthogonal (perpendicular)!
#Vectors #LinearAlgebra #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar value representing how much two vectors point in the same direction.
Ex: `[a,b] . [c,d] = ac + bd`
Pro-Tip: If the dot product is zero, the vectors are orthogonal (perpendicular)!
#Vectors #LinearAlgebra #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar value representing how much two vectors point in the same direction.
Ex: `[a,b] . [c,d] = ac + bd`
Pro-Tip: If the dot product is zero, the vectors are orthogonal (perpendicular)!
#Vectors #LinearAlgebra #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar value representing how much two vectors point in the same direction.
Ex: `[a,b] . [c,d] = ac + bd`
Pro-Tip: If the dot product is zero, the vectors are orthogonal (perpendicular)!
#Vectors #LinearAlgebra #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar value representing how much two vectors point in the same direction.
Ex: `[a,b] . [c,d] = ac + bd`
Pro-Tip: If the dot product is zero, the vectors are orthogonal (perpendicular)!
#Vectors #LinearAlgebra #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar showing how much two vectors align.
Ex: `v=[1,2], u=[3,4]`. `v.u = 1*3 + 2*4 = 11`.
Pro-Tip: If `v.u = 0`, vectors are perpendicular! Great for checking orthogonality.
#LinearAlgebra #Vectors #STEM #StudyNotes