# matrixcalc v1.0-3

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## Collection of functions for matrix calculations

A collection of functions to support matrix calculations for probability, econometric and numerical analysis. There are additional functions that are comparable to APL functions which are useful for actuarial models such as pension mathematics. This package is used for teaching and research purposes at the Department of Finance and Risk Engineering, New York University, Polytechnic Institute, Brooklyn, NY 11201.

## Functions in matrixcalc

 Name Description matrix.inverse Inverse of a square matrix is.non.singular.matrix Test if matrix is non-singular frobenius.prod Frobenius innter product of matrices stirling.matrix Stirling Matrix direct.prod Direct prod of two arrays lower.triangle Lower triangle portion of a matrix frobenius.matrix Frobenius Matrix is.positive.semi.definite Test matrix for positive semi-definiteness is.skew.symmetric.matrix Test for a skew-symmetric matrix fibonacci.matrix Fibonacci Matrix is.indefinite Test matrix for positive indefiniteness hankel.matrix Hankel Matrix duplication.matrix Duplication matrix for n by n matrices svd.inverse SVD Inverse of a square matrix hilbert.matrix Hilbert matrices H.matrices List of H Matrices matrix.trace The trace of a matrix E.matrices List of E Matrices frobenius.norm Compute the Frobenius norm of a matrix is.positive.definite Test matrix for positive definiteness shift.left Shift a matrix n columns to the left direct.sum Direct sum of two arrays L.matrix Construct L Matrix N.matrix Construct N Matrix K.matrix K Matrix elimination.matrix Elimination matrix for lower triangular matrices symmetric.pascal.matrix Symmetric Pascal matrix entrywise.norm Compute the entrywise norm of a matrix %s% Direct sum of two arrays commutation.matrix Commutation matrix for r by c numeric matrices shift.down Shift matrix m rows down is.negative.semi.definite Test matrix for negative semi definiteness is.square.matrix Test for square matrix matrix.power Matrix Raised to a Power upper.triangle Upper triangle portion of a matrix u.vectors u vectors of an identity matrix spectral.norm Spectral norm of matrix D.matrix Duplication matrix one.norm Compute the one norm of a matrix T.matrices List of T Matrices creation.matrix Creation Matrix inf.norm Compute the infinitity norm of a matrix maximum.norm Maximum norm of matrix is.diagonal.matrix Test for diagonal square matrix is.symmetric.matrix Test for symmetric numeric matrix lu.decomposition LU Decomposition of Square Matrix vandermonde.matrix Vandermonde matrix matrix.rank Rank of a square matrix hadamard.prod Hadamard product of two matrices pascal.matrix Pascal matrix shift.up Shift matrix m rows up is.negative.definite Test matrix for negative definiteness set.submatrix Store matrix inside another matrix shift.right Shift matrix n columns to the right toeplitz.matrix Toeplitz Matrix vec Vectorize a matrix is.idempotent.matrix Test for idempotent square matrix vech Vectorize a matrix hilbert.schmidt.norm Compute the Hilbert-Schmidt norm of a matrix is.singular.matrix Test for singular square matrix No Results!