There are a number of functions which take matrices as arguments or yield matrices as return values. SF[1], SF[2], Option variable: dot0nscsimp Default value: true. When matrixp is not given an optional argument, return true if e is a matrix. If x is a list of lists, the algorithm is applied to the sublists, which must have equal numbers of elements. The other flags see eigenvalues and eigenvectors have the same effects since similaritytransform calls the other functions in the package in order to be able to form rightmatrix. Return the p -norm matrix condition number of the matrix m. If the flag hermitianmatrix is true then leftmatrix is the complex conjugate of the transpose of rightmatrix. Function: vectorsimp expr Applies simplifications and expansions according to the following global flags:.

When the operands are 1-column or 1-row matrices a and b, the expression a.b is Maxima loads the package automatically if one of the functions eigenvalues or Returns x /norm(x); this is a unit vector in the same direction as x. Maxima Manual: linearalgebra. Return a copy of the Maxima expression e.

Video: Wxmaxima matrix norms LAFF-NLA: Matrix Norms

Although e can . Return the p -norm matrix condition number of the matrix m. Dual Norms for Dual Matrix Spaces, and Norms for Bilinear Forms There are analogous ratio-maxima for m-by-n Matrix norms; for instance.

If M doesn't have a column i or jsignal an error. When n isn't a positive integer, signal an error. Option variable: dot1simp Default value: true. Diagonal 2. Given an optional argument preturn true if e is a matrix and p evaluates to true for every matrix element.

## Maxima Manual linearalgebra

Members of the field needn't be Maxima expressions.

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To compute the factorization, the first task is to convert each matrix entry to a member of the indicated field. The function algsys is used here to solve for the eigenvectors. Floating point addition arithmetic isn't associative, so the meaning of 'field' differs from the mathematical definition. If M is not a block matrix, return true if is equal e0 is true for each element e of the matrix M. Video: Wxmaxima matrix norms Scientific Computing 09 -- Matrix Norms The third item is false or the matrix of right singular vectors. |

Maxima Manual: linearalgebra.

## Maxima Manual Matrices and Linear Algebra

Return the p -norm matrix condition number of the matrix m. The allowed values for p are 1 and inf. (%i4) mat_fullunblocker (%); (%o4) mat_function (function, matrix) returns an The allowed values for p are 1, inf, and frobenius (Frobenius matrix norm).

The first argument M should be a square matrix or a non-matrix.

If knowneigvects is set to true and the list of eigenvectors is given the setting of the flag nondiagonalizable may not be correct.

The default for row is complex conjugate of col. Computes the singular value decomposition SVD of a matrix Acomprising the singular values and, optionally, the left and right singular vectors.

### matrix 2norm and associated matrix condition number

The i, j -th element of the Hessian matrix is diff fx [i], 1, x [j], 1.

Wxmaxima matrix norms |
To compute the factorization, the first task is to convert each matrix entry to a member of the indicated field.
When dotscrules is truean expression A. When doscmxplus is truescalar-matrix operations yield a matrix result. Function: triangularize M Returns the upper triangular form of the matrix M. A list of three items is returned. Option variable: dontfactor Default value: []. If M doesn't have a row i or jsignal an error. |

All The computed eigenvectors are normalized to have Euclidean norm equal to 1. -norm is difficult for p>1 since it is a nonlinear optimization problem with constraints.

### Matrix Norm from Wolfram MathWorld

Matrix norms are implemented as Norm[m, p], where p may be 1, 2, Infinity. Dear experts, AFAIK maxima currently has no matrix 2-norm and no matrix condition number based on 2-norm. In teaching the 2-norm/2-condition sometimes.

When the operands are more general matrices, the product is the matrix product a and b.

When M is a matrix, each entry of M can be a square matrix - thus M can be a blocked Maxima matrix. If M is a matrix, swap columns i and j. The first argument M should be a square matrix or a non-matrix.

Returns the Hessian matrix of f with respect to the list of variables x. Returns the Hessian matrix of f with respect to the list of variables x.

Function: nonscalarp expr Returns true if expr is a non-scalar, i. Invert a matrix M by using the LU factorization.

The other flags see eigenvalues and eigenvectors have the same effects since similaritytransform calls the other functions in the package in order to be able to form rightmatrix.

The third item is false or the matrix of right singular vectors. The function f must accept any number of arguments a Maxima nary function.

If the flag hermitianmatrix is true then leftmatrix is the complex conjugate of the transpose of rightmatrix.