D.3.1 matrix_lib

Library:

matrix.lib

Purpose:

Elementary Matrix Operations

Procedures:

D.3.1.1 compress		matrix, zero columns from A deleted
D.3.1.2 concat		matrix, concatenation of matrices A1,A2,...
D.3.1.3 diag		matrix, nxn diagonal matrix with entries poly p
D.3.1.4 dsum		matrix, direct sum of matrices A1,A2,...
D.3.1.5 flatten		ideal, generated by entries of matrix A
D.3.1.6 genericmat		generic nxm matrix [entries from id]
D.3.1.7 is_complex		1 if list c is a complex, 0 if not
D.3.1.8 outer		matrix, outer product of matrices A and B
D.3.1.9 power		matrix/intmat, n-th power of matrix/intmat A
D.3.1.10 skewmat		generic skew-symmetric nxn matrix [entries from id]
D.3.1.11 submat		submatrix of A with rows/cols specified by intvec r/c
D.3.1.12 symmat		generic symmetric nxn matrix [entries from id]
D.3.1.13 unitmat		unit square matrix of size n
D.3.1.14 gauss_col		transform a matrix into col-reduced Gauss normal form
D.3.1.15 gauss_row		transform a matrix into row-reduced Gauss normal form
D.3.1.16 addcol		add p*(c1-th col) to c2-th column of matrix A, p poly
D.3.1.17 addrow		add p*(r1-th row) to r2-th row of matrix A, p poly
D.3.1.18 multcol		multiply c-th column of A with poly p
D.3.1.19 multrow		multiply r-th row of A with poly p
D.3.1.20 permcol		permute i-th and j-th columns
D.3.1.21 permrow		permute i-th and j-th rows
D.3.1.22 rowred		reduction of matrix A with elementary row-operations
D.3.1.23 colred		reduction of matrix A with elementary col-operations
D.3.1.24 linear_relations		find linear relations between homogeneous vectors
D.3.1.25 rm_unitrow		remove unit rows and associated columns of A
D.3.1.26 rm_unitcol		remove unit columns and associated rows of A
D.3.1.27 headStand		A[n-i+1,m-j+1]:=A[i,j]
D.3.1.28 symmetricBasis		basis of k-th symmetric power of n-dim v.space
D.3.1.29 exteriorBasis		basis of k-th exterior power of n-dim v.space
D.3.1.30 symmetricPower		k-th symmetric power of a module/matrix A
D.3.1.31 exteriorPower		k-th exterior power of a module/matrix A