Mathematical Experiment 5

When the command ``with linalg'' is issued, over 100 new functions are defined. Look for ``references'' under help for further details. These functions may be divided into several categories:

  creation of matrices

hilbert, vandermonde, toeplitz, fibonacci, randmat, diag, matrix, entermatrix, blockmatrix, JordanBlock

  creation of a vector

vector, randvector, col, row

  scalar value associated with a vector

norm

  scalar value associated with two vectors

angle, dotprod, innderprod

  scalar value associated with a matrix

det, trace, permanent, norm, singularvals, cond, vectdim, rowdim, coldim, rank, hadamard

  vector associated with two vectors

crossprod

  vector associated with one matrix

eigenvect, subvector, row

  operation on a matrix

delrows, delcols, addcol, addrow, swapcol, mulcol, swaprow, adj, adjoint, extend, copyinto, augment

  matrix associated with a vector

band, toeplitz, vandermonde

  matrix associated with one matrix

submatrix, adj, adjoint, transpose, htranspose, exponential, minor, inverse

  matrix associated with two matrices

matadd, multiply, extend

  test the property

equal, issimilar, iszero, orthog, definite

  calculus of several variables

grad, curl, potential, vecpotent, jacobian, laplacian, curl, diverge, hessian

  operations related to the eigenvalue

charmat, charpoly, eigenvect, eigenvals

  operations related to the polynomial

charpoly, companion, minpoly, sylvester, bezout

  creation of matrix function from a vector function

wronskian

  stack operation

stack

  normal form of a matrix

smith, ismith, hermit, ihermit, jordan

  basis computation

basis, colspace, rowspace, rowspan, colspan, sumbasis, intbasis, kernel

  computation of orthogonal vectors

GramSchmidt, normalize

  matrix decomposition

LUdecomp, QRdecomp, cholesky, gaussjord, frobenius

  solving linear system

backsub, guasselim, forwardsub, linsolve, ffgausselim, pivot, geneqns, genmatrix, leastsqrs

exp5.tex