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Functions of Matrices

Roger B. Kirchner
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Defines a function, MatrixReplace, to evaluate an expression at a matrix using a generalization of a formula in R. B. Kirchner, "An Explicit Formula for e^(A t)", American Mathematical Monthly, Vol 74, No 10, December 1967.

For example, let A be a square matrix. MatrixReplace[f[x], x -> A] returns f[A], where multiplication is matrix multiplication. MatrixReplace[E^(x t), x -> A] returns the matrix exponential of A t. MatrixReplace[x^n, x -> A] returns the nth matrix power of A.

*Mathematics > Algebra > Linear Algebra

Algebra, Eigen value, Eigen vector, Matrix exponential, Matrix multiplication, Matrix operations, Matrix replace, MatrixPower, MatrixReplace, MatrixReplace.m
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MatrixReplace.m (4.4 KB) - Mathematica Package