#matrixmath — Public Fediverse posts
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Alright, future engineers!
**Matrix Addition:** Combine matrices by adding their corresponding elements.
Ex: If A=[1,2;3,4] & B=[5,6;7,8], then A+B = [6,8;10,12].
Pro-Tip: They MUST have the same dimensions to add them!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Matrix Addition:** Combine matrices by adding their corresponding elements.
Ex: If A=[1,2;3,4] & B=[5,6;7,8], then A+B = [6,8;10,12].
Pro-Tip: They MUST have the same dimensions to add them!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Determinant:** A scalar from a square matrix, showing its 'scaling factor'.
Ex: For `[[a,b],[c,d]]`, `det = ad-bc`.
Pro-Tip: If `det = 0`, the matrix is singular & has no inverse!
#MatrixMath #LinAlg #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication:** Produces a new matrix by combining rows of the first with columns of the second.
Ex: For `C = AB`, `C_ij = sum(A_ik * B_kj)`.
Pro-Tip: Inner dimensions MUST match! `(m x n) * (n x p)` gives `(m x p)`.
#MatrixMath #LinearAlgebra #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication:** Produces a new matrix by combining rows of the first with columns of the second.
Ex: For `C = AB`, `C_ij = sum(A_ik * B_kj)`.
Pro-Tip: Inner dimensions MUST match! `(m x n) * (n x p)` gives `(m x p)`.
#MatrixMath #LinearAlgebra #STEM #StudyNotes -
Alright, future engineers!
**Inverse Matrix:** A matrix `A_inv` that, when multiplied by `A`, yields the identity matrix `I`.
Ex: If `A * A_inv = I`.
Pro-Tip: Use `A_inv` to solve `Ax=b` for `x = A_inv * b`. Super powerful for system analysis!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Inverse Matrix:** A matrix `A_inv` that, when multiplied by `A`, yields the identity matrix `I`.
Ex: If `A * A_inv = I`.
Pro-Tip: Use `A_inv` to solve `Ax=b` for `x = A_inv * b`. Super powerful for system analysis!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication:** Combines two matrices. Columns of 1st *must* equal rows of 2nd for it to work!
Ex: `A(m x n) * B(n x p) -> C(m x p)`.
Pro-Tip: Order matters! `A*B` is generally NOT `B*A`. Crucial for transformations!
#MatrixMath #LinearAlgebra #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication:** Combines two matrices. Columns of 1st *must* equal rows of 2nd for it to work!
Ex: `A(m x n) * B(n x p) -> C(m x p)`.
Pro-Tip: Order matters! `A*B` is generally NOT `B*A`. Crucial for transformations!
#MatrixMath #LinearAlgebra #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication:** Combines linear transformations.
Ex: `(AB)_ij = Sum(A_ik * B_kj)`
Pro-Tip: Order matters! `AB != BA` generally. Don't assume commutativity!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication:** Combines linear transformations.
Ex: `(AB)_ij = Sum(A_ik * B_kj)`
Pro-Tip: Order matters! `AB != BA` generally. Don't assume commutativity!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Determinant:** A scalar value from a square matrix. If it's non-zero, the matrix is invertible!
Ex: For a 2x2 matrix `[[a,b],[c,d]]`, `det = ad - bc`.
Pro-Tip: If `det(A)=0`, A is singular (no inverse) & its columns are linearly dependent!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Determinant:** A scalar value from a square matrix. If it's non-zero, the matrix is invertible!
Ex: For a 2x2 matrix `[[a,b],[c,d]]`, `det = ad - bc`.
Pro-Tip: If `det(A)=0`, A is singular (no inverse) & its columns are linearly dependent!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Matrix Addition: Sums matrices by adding corresponding elements. Dimensions MUST match!
Ex: `[[1,2],[3,4]] + [[5,6],[7,8]] = [[6,8],[10,12]]`
Pro-Tip: If dimensions differ, addition is undefined! Crucial for compatibility in systems.
#MatrixMath #LinearAlgebra #STEM #StudyNotes -
Matrix Addition: Sums matrices by adding corresponding elements. Dimensions MUST match!
Ex: `[[1,2],[3,4]] + [[5,6],[7,8]] = [[6,8],[10,12]]`
Pro-Tip: If dimensions differ, addition is undefined! Crucial for compatibility in systems.
#MatrixMath #LinearAlgebra #STEM #StudyNotes -
Alright, future engineers!
**Identity Matrix (I):** Acts like the number '1' for matrices.
Ex: Multiplying any matrix A by I gives A back: `A*I = I*A = A`.
Pro-Tip: It's square, with 1s on the main diagonal & 0s elsewhere. Essential for inverse ops!
#MatrixMath #LinearAlgebra #STEM #StudyNotes -
Alright, future engineers!
**Identity Matrix (I):** Acts like the number '1' for matrices.
Ex: Multiplying any matrix A by I gives A back: `A*I = I*A = A`.
Pro-Tip: It's square, with 1s on the main diagonal & 0s elsewhere. Essential for inverse ops!
#MatrixMath #LinearAlgebra #STEM #StudyNotes -
Alright, future engineers!
**Determinant:** A scalar value from a square matrix. Reveals invertibility & volume scaling.
Ex: For `[[a,b],[c,d]]`, `det(A) = ad - bc`.
Pro-Tip: If `det(A) = 0`, the matrix is singular & its columns are linearly dependent!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Determinant:** A scalar value from a square matrix. Reveals invertibility & volume scaling.
Ex: For `[[a,b],[c,d]]`, `det(A) = ad - bc`.
Pro-Tip: If `det(A) = 0`, the matrix is singular & its columns are linearly dependent!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Matrix Transpose (Aᵀ):** Flips a matrix over its diagonal, turning its rows into columns & vice versa.
Ex: If `A = [[1,2],[3,4]]`, then `Aᵀ = [[1,3],[2,4]]`.
Pro-Tip: For product `(AB)ᵀ = BᵀAᵀ` (note the flipped order!)
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Matrix Transpose (Aᵀ):** Flips a matrix over its diagonal, turning its rows into columns & vice versa.
Ex: If `A = [[1,2],[3,4]]`, then `Aᵀ = [[1,3],[2,4]]`.
Pro-Tip: For product `(AB)ᵀ = BᵀAᵀ` (note the flipped order!)
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Elementary Row Ops:** Operations to transform a matrix (swap rows, scale rows, add rows).
Ex: `R1 <-> R2` (swap row 1 & row 2).
Pro-Tip: Key for solving systems of equations or finding matrix inverses!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Elementary Row Ops:** Operations to transform a matrix (swap rows, scale rows, add rows).
Ex: `R1 <-> R2` (swap row 1 & row 2).
Pro-Tip: Key for solving systems of equations or finding matrix inverses!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication:** Creates a new matrix where each entry is the dot product of a row from the 1st and a col from the 2nd.
Ex: `(AB)_ij = sum(A_ik * B_kj)`
Pro-Tip: The # of columns in the first matrix MUST equal the # of rows in the second!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication:** Creates a new matrix where each entry is the dot product of a row from the 1st and a col from the 2nd.
Ex: `(AB)_ij = sum(A_ik * B_kj)`
Pro-Tip: The # of columns in the first matrix MUST equal the # of rows in the second!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Matrix Transpose:** Switches a matrix's rows & columns.
Ex: If `A = [[1,2],[3,4]]`, then `A^T = [[1,3],[2,4]]`.
Pro-Tip: Dimensions flip! An `m x n` matrix becomes `n x m`.
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Matrix Transpose:** Switches a matrix's rows & columns.
Ex: If `A = [[1,2],[3,4]]`, then `A^T = [[1,3],[2,4]]`.
Pro-Tip: Dimensions flip! An `m x n` matrix becomes `n x m`.
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Determinant:** A scalar from a square matrix, indicating if it's invertible.
Ex: For `A = [[a,b],[c,d]]`, `det(A) = ad - bc`.
Pro-Tip: If `det(A) = 0`, the matrix is singular (no inverse exists!).
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Determinant:** A scalar from a square matrix, indicating if it's invertible.
Ex: For `A = [[a,b],[c,d]]`, `det(A) = ad - bc`.
Pro-Tip: If `det(A) = 0`, the matrix is singular (no inverse exists!).
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
The **Identity Matrix (I)** acts like the number '1' for matrix multiplication.
Ex: `A * I = A`. For 2x2: `I = [[1,0],[0,1]]`.
Pro-Tip: It's always square & has 1s on the main diagonal, 0s everywhere else.
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
The **Identity Matrix (I)** acts like the number '1' for matrix multiplication.
Ex: `A * I = A`. For 2x2: `I = [[1,0],[0,1]]`.
Pro-Tip: It's always square & has 1s on the main diagonal, 0s everywhere else.
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Identity Matrix (I):** A square matrix with 1s on the main diagonal & 0s elsewhere.
Ex: `I_2 = [[1,0],[0,1]]`
Pro-Tip: It's the '1' of matrix multiplication! `A*I = I*A = A`.
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Identity Matrix (I):** A square matrix with 1s on the main diagonal & 0s elsewhere.
Ex: `I_2 = [[1,0],[0,1]]`
Pro-Tip: It's the '1' of matrix multiplication! `A*I = I*A = A`.
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
The **Identity Matrix (I)** is a square matrix with 1s on the main diagonal & 0s elsewhere.
Ex: For 2x2, `I = [[1,0],[0,1]]`.
Pro-Tip: It's the 1 of matrix multiplication – `AI = IA = A`. Essential for inverses!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
The **Identity Matrix (I)** is a square matrix with 1s on the main diagonal & 0s elsewhere.
Ex: For 2x2, `I = [[1,0],[0,1]]`.
Pro-Tip: It's the 1 of matrix multiplication – `AI = IA = A`. Essential for inverses!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
A **Determinant** is a scalar value that provides properties of a square matrix (e.g., if it's invertible).
Ex: For `A = [[a,b],[c,d]]`, `det(A) = ad - bc`.
Pro-Tip: If `det(A) = 0`, the matrix is singular (no inverse)! -
Alright, future engineers!
A **Determinant** is a scalar value that provides properties of a square matrix (e.g., if it's invertible).
Ex: For `A = [[a,b],[c,d]]`, `det(A) = ad - bc`.
Pro-Tip: If `det(A) = 0`, the matrix is singular (no inverse)! -
Alright, future engineers!
The **Determinant** of a square matrix reveals its scaling factor under transformation. Ex: For `[[a,b],[c,d]]`, det = `ad - bc`. Pro-Tip: If det != 0, the matrix is invertible & its columns are linearly independent!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
The **Determinant** of a square matrix reveals its scaling factor under transformation. Ex: For `[[a,b],[c,d]]`, det = `ad - bc`. Pro-Tip: If det != 0, the matrix is invertible & its columns are linearly independent!
#LinearAlgebra #MatrixMath #STEM #StudyNotes -
Alright, future engineers!
**Matrix Multiplication:** Combines two matrices, like applying transformations in sequence. Ex: For C=AB, C_ij = sum(A_ik * B_kj). Pro-Tip: Order matters! AB != BA (usually).
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Alright, future engineers!
**Matrix Multiplication:** Combines two matrices, like applying transformations in sequence. Ex: For C=AB, C_ij = sum(A_ik * B_kj). Pro-Tip: Order matters! AB != BA (usually).
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Alright, future engineers!
A **Determinant** is a scalar value from a square matrix, indicating if it's invertible. Ex: For A=[[a,b],[c,d]], det(A)=ad-bc. Pro-Tip: If det(A)=0, the matrix is singular – it has no inverse! -
Alright, future engineers!
A **Determinant** is a scalar value from a square matrix, indicating if it's invertible. Ex: For A=[[a,b],[c,d]], det(A)=ad-bc. Pro-Tip: If det(A)=0, the matrix is singular – it has no inverse! -
Alright, future engineers!
The determinant (det(A)) of a square matrix is a scalar value that tells us about its invertibility & volume scaling. Ex: For A=[a,b;c,d], det(A)=ad-bc. Pro-Tip: If det(A)=0, A is singular (non-invertible)! Crucial info.
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Alright, future engineers!
The determinant (det(A)) of a square matrix is a scalar value that tells us about its invertibility & volume scaling. Ex: For A=[a,b;c,d], det(A)=ad-bc. Pro-Tip: If det(A)=0, A is singular (non-invertible)! Crucial info.
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Researchers upend AI status quo by eliminating matrix multiplication in LLMs - Enlarge / Illustration of a brain inside of a light bulb. (credit: Gett... - https://arstechnica.com/?p=2033314 #matrixmultiplication #machinelearning #googlegemini #ucsantacruz #matrixmath #chatgpt #ternary #biz #matmul #gpu #ai
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Researchers upend AI status quo by eliminating matrix multiplication in LLMs - Enlarge / Illustration of a brain inside of a light bulb. (credit: Gett... - https://arstechnica.com/?p=2033314 #matrixmultiplication #machinelearning #googlegemini #ucsantacruz #matrixmath #chatgpt #ternary #biz #matmul #gpu #ai
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Ummm...this is totally gonna fuck #NVidia's share value! 😂😂😂
That's what they get when they rely on throwing hardware at an issue when you could've fixed the software algorithms! #AI #MatMul #MatrixMath