# Review of Linear Algebra

2021-10-20

Math

336

Matrix
Basic Operations
Matrix Product (Dot Product)
Matrix Division
Matrix Multiplication (Hadamard Product)
Matrix Operations
Matrix Transpose
Matrix Inversion
Matrix Trace (the sum of the main diagonal elements)
Matrix Determinant
Matrix Rank (the maximum number of linearly independent columns)
Matrix Factorization (?)
LU Decomposition
QR Decomposition
Eigendecomposition
Singular Value Decomposition
Ref: Linear Algebra Cheat Sheet Python Code
Others:
Unitary Matrix
A matrix that satisfies
Minor Matrix
Adjugate Matrix
For square matrix A, , , where is the (i, j) minor of A.
Conjugate Transpose
, for complex number ,
Orthogonal Matrix
A matrix that satisfy
Matrix Product
Matrix product is produced by taking i-th row of the first matrix and j-th column of the second matrix and calculate dot product of the two vectors as the (i, j) element in the result matrix.
Given
then,
Matrix Division
Matrix Division makes use of the following property:
where