Matrix Addition | Combines two matrices of the same size into a new matrix by adding corresponding elements |
Matrix Subtraction | Similar to matrix addition, but subtracts corresponding elements |
Matrix-Scalar Multiplication | Multiplies every element of the matrix by a scalar |
Matrix Multiplication | Combines two matrices into a new matrix, where each value is calculated from the sum of multiplications from the corresponding row and column |
Determinant Calculation | The determinant is a special number that can be calculated from a square matrix |
Matrix Inversion | The process of finding the matrix that, when multiplied with the initial matrix, gives an identity matrix |
Transpose of a Matrix | Operation that flips a matrix over its diagonal, changing row and column indices for each element |
Eigenvalue and Eigenvector Computation | Eigenvalues/vectors are fundamental to power methods, finding principal components in matrices, etc |
Gaussian Elimination | An algorithm for solving linear systems of equations |
LU Decomposition | Decomposes a matrix as the product of lower and upper triangular matrices |
QR Decomposition | Decomposes a matrix into an orthogonal matrix and an upper triangular matrix |
Cholesky Decomposition | Decomposes a Hermitian, positive-definite matrix into product of lower triangular matrix and its conjugate transpose |
Singular Value Decomposition | Expresses a matrix as the product of two orthogonal matrices and a diagonal matrix |
Gram-Schmidt Process | Orthogonalizes a set of vectors in an inner product space |
Gauss-Jordan Elimination | Algorithm that can be used to solve systems of linear equations and find the rank of a matrix |
Jacobi Eigenvalue Algorithm | Iterative method to calculate eigenvalues of a real symmetric matrix |
Power Iteration | Procedure to calculate dominant eigenvalue and corresponding eigenvector of a square matrix |
Tridiagonal Matrix Algorithm (Thomas algorithm) | Algorithm to solve tridiagonal systems of equations |
Strassen Algorithm | Efficient algorithm to multiply two matrices |
Givens Rotation | Used in certain QR decomposition methods to zero out certain elements |
