# Matrix Math and Special Matrices

 { } Array Construction Create a series or multiple column array *^ (Matrix Multiply) Multiply two matrices \^ (Matrix Solve) Matrix solve /^ (Matrix Right Division) Matrix right division ^^ (Matrix Power) Raise a matrix to a power ' (Matrix Transpose) Swap the rows and columns of a specified table ~^ (Conjugate Transpose) Complex conjugate transpose BALANCE Balance a matrix CHOLESKY Compute the Cholesky factorization of a square matrix COLNOS Return an array of COL numbers COND Estimate the condition number of a matrix CROSSPROD Calculate the matrix cross product DET Calculate matrix determinant DIAGONAL Get the main diagonal of a matrix EIG Compute the eigenvalues and eigenvectors of a square matrix EIGVAL Get eigenvalues of a matrix EIGVEC Get eigenvectors of a matrix EXPM Calculate the exponential of a matrix FUNM Calculate a general matrix function HANKEL Generate a Hankel matrix HESS Find the Hessenberg form of a matrix INNERPROD Matrix Inner Product INTERPOSE Apply REDUCE associatively INVERSE Invert a matrix KRON Compute the Kronecker tensor product LLU Lower triangular matrix in LU decomposition LOGM Calculate the matrix log LOTRI Return the lower triangle of a matrix including the main diagonal LOTRIX Return the lower triangle of a matrix excluding the main diagonal LU LU decomposition MDIV Matrix solve MMULT Matrix multiplication NBEIGVAL Get eigenvalues without balancing step NBEIGVEC Get eigenvectors without balancing step NORM Calculate the norm of a series or array NULL Compute an orthogonal basis for the Null space of an array NUMEL Total number of matrix elements ORTH Compute an orthonormal basis of an array using SVD OUTERPROD Outer product of two vectors PARTPROD Partial product of two vectors PINV Calculate the pseudo inverse of a matrix using SVD QR QR decomposition RANK Estimate the number of independent rows or columns of an array RCOND Estimate the reciprocal condition number ROWNOS Return an array of row numbers SCHUR Generate the SCHUR form of a matrix SIZE Return a 2 point series containing the dimensions of an array SQRTM Calculate the matrix square root SVD Singular value decomposition TOEPLITZ Generate a Toeplitz matrix TRACE Calculate the trace of an array, the sum of the diagonal elements TRANSPOSE Transpose a matrix TRANSPOSECONJ Conjugate transpose a matrix TRIL Lower triangular matrix TRIU Upper triangular matrix ULU Upper triangular matrix in LU decomposition UPTRI Return the upper triangle of a matrix including the main diagonal UPTRIX Return the upper triangle of a matrix excluding the main diagonal USCHUR Compute the SCHUR form of an input matrix VANDER Generate a Vandermonde matrix