This app provides a collection of operations that can help you: Matrix addition, matrix subtraction, Matrix Multiplication, Transpose, Determinet, LU decomposition, Cholesky decomposition, Singular value decomposition, and Linear Transformations (eigenvectors and eigenvalues).

default-2023

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a_12

b_11

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c_21

input_22

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matrix_addition

multiply

find_subtraction_of_two_matrix

svd_a

trans_b

det_b

det_c

trans_c

chole_decom

eig_b

a_33

eig_c

orthogonal_a

eig_a

LU decomposition (also known as lower-upper decomposition or LU factorization) is a factorization of a matrix into the product of a lower triangular matrix and an upper triangular matrix.{{ "D*X=E" | katex }}

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This method decomposes a positive-definite matrix into a lower triangular matrix (L) and its transpose. It is often used for solving systems of linear equations and for simulating random variables. A matrix is positive definite if it is symmetric (i.e., the elements on the main diagonal are the same as the elements in the same position on the other diagonal) and all of its eigenvalues are positive. The Cholesky decomposition can only be applied to positive definite matrices. <img src="data:image/png;base64,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" alt="Cholesky Decomposition -- from Wolfram MathWorld">

The singular value decomposition (SVD) is a factorization of a real or complex matrix that generalizes the eigendecomposition of a positive definite normal matrix to any m-by-n matrix via an extension of the polar decomposition. The SVD decomposes a matrix A into the product of three matrices: U, S, and V*:{{ "A = U * S * V^*" | katex }} <img src="https://miro.medium.com/max/894/1*XNWUlrQJXGeoCDqUMd0iUA.png" alt="A Beginner's Guide to Singular Value Decomposition (SVD) | by Mukundh Murthy | Medium" width="369">

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