Review of Linear Algebra

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