• Home
    Tables – Mathematics – Linear Algebra Algorithms

    Matrix AdditionCombines two matrices of the same size into a new matrix by adding corresponding elements
    Matrix SubtractionSimilar to matrix addition, but subtracts corresponding elements
    Matrix-Scalar MultiplicationMultiplies every element of the matrix by a scalar
    Matrix MultiplicationCombines two matrices into a new matrix, where each value is calculated from the sum of multiplications from the corresponding row and column
    Determinant CalculationThe determinant is a special number that can be calculated from a square matrix
    Matrix InversionThe process of finding the matrix that, when multiplied with the initial matrix, gives an identity matrix
    Transpose of a MatrixOperation that flips a matrix over its diagonal, changing row and column indices for each element
    Eigenvalue and Eigenvector ComputationEigenvalues/vectors are fundamental to power methods, finding principal components in matrices, etc
    Gaussian EliminationAn algorithm for solving linear systems of equations
    LU DecompositionDecomposes a matrix as the product of lower and upper triangular matrices
    QR DecompositionDecomposes a matrix into an orthogonal matrix and an upper triangular matrix
    Cholesky DecompositionDecomposes a Hermitian, positive-definite matrix into product of lower triangular matrix and its conjugate transpose
    Singular Value DecompositionExpresses a matrix as the product of two orthogonal matrices and a diagonal matrix
    Gram-Schmidt ProcessOrthogonalizes a set of vectors in an inner product space
    Gauss-Jordan EliminationAlgorithm that can be used to solve systems of linear equations and find the rank of a matrix
    Jacobi Eigenvalue AlgorithmIterative method to calculate eigenvalues of a real symmetric matrix
    Power IterationProcedure to calculate dominant eigenvalue and corresponding eigenvector of a square matrix
    Tridiagonal Matrix Algorithm (Thomas algorithm)Algorithm to solve tridiagonal systems of equations
    Strassen AlgorithmEfficient algorithm to multiply two matrices
    Givens RotationUsed in certain QR decomposition methods to zero out certain elements