#vectorspaces — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #vectorspaces, aggregated by home.social.
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Alright, future engineers!
**Linear Independence:** Vectors are LI if no vector can be expressed as a linear combo of the others.
Ex: For `c1*v1 + c2*v2 = 0`, only `c1=c2=0` works.
Pro-Tip: LI vectors are unique & don't introduce redundant info. Key for basis & unique solutions!
#LinearAlgebra #VectorSpaces #STEM #StudyNotes -
Alright, future engineers!
**Linear Independence:** Vectors are LI if no vector can be expressed as a linear combo of the others.
Ex: For `c1*v1 + c2*v2 = 0`, only `c1=c2=0` works.
Pro-Tip: LI vectors are unique & don't introduce redundant info. Key for basis & unique solutions!
#LinearAlgebra #VectorSpaces #STEM #StudyNotes -
**Linear Independence (LI):** Vectors are LI if none can be formed by scaling/adding the others.
Ex: If `c1*v1 + c2*v2 = 0` only when `c1=c2=0`.
Pro-Tip: LI vectors are fundamental for forming a *basis* for a vector space!
#LinearAlgebra #VectorSpaces #STEM #StudyNotes -
**Linear Independence (LI):** Vectors are LI if none can be formed by scaling/adding the others.
Ex: If `c1*v1 + c2*v2 = 0` only when `c1=c2=0`.
Pro-Tip: LI vectors are fundamental for forming a *basis* for a vector space!
#LinearAlgebra #VectorSpaces #STEM #StudyNotes -
Alright, future engineers!
**Linear Combination:** A sum of vectors scaled by scalars.
Ex: `c1*v1 + c2*v2` creates a new vector from `v1` & `v2`.
Pro-Tip: Think of it as mixing vectors. It's how basis vectors build *any* vector in their space!
#LinearAlgebra #VectorSpaces #STEM #StudyNotes -
Alright, future engineers!
**Linear Combination:** A sum of vectors scaled by scalars.
Ex: `c1*v1 + c2*v2` creates a new vector from `v1` & `v2`.
Pro-Tip: Think of it as mixing vectors. It's how basis vectors build *any* vector in their space!
#LinearAlgebra #VectorSpaces #STEM #StudyNotes -
Alright, future engineers!
**Linear Combination:** A sum of vectors, each multiplied by a scalar.
Ex: `c1*v1 + c2*v2`.
Pro-Tip: Crucial for understanding span & basis! Think of mixing vectors.
#LinearAlgebra #VectorSpaces #STEM #StudyNotes -
Alright, future engineers!
**Linear Combination:** A sum of vectors, each multiplied by a scalar.
Ex: `c1*v1 + c2*v2`.
Pro-Tip: Crucial for understanding span & basis! Think of mixing vectors.
#LinearAlgebra #VectorSpaces #STEM #StudyNotes -
Alright, future engineers!
A **Basis** is a minimal set of linearly independent vectors that can create any other vector in a vector space. Ex: For R^2, `{[1,0], [0,1]}` is a standard basis. Pro-Tip: Think of them as the essential building blocks for that space!
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Alright, future engineers!
A **Basis** is a minimal set of linearly independent vectors that can create any other vector in a vector space. Ex: For R^2, `{[1,0], [0,1]}` is a standard basis. Pro-Tip: Think of them as the essential building blocks for that space!