print 1 minute | Arithmetic | Analysis | Geometry | Statistics | Menus, icons,... Mathematical Objects | Linear algebra | Functions | 2D Graphics | Combinatorics | Toolbar WIRIS ++ | Equations and systems of equations | Progressions | 3D Graphics | Units of measurement | Primary
Linear algebra

The fundamental tools of linear algebra are vectors and matrices, which are addressed in the chapter, Mathematical Objects. This chapter deals with the operations that can be carried out on vectors and matrices and other functions that take them as arguments.

 >>fast Operations plus subtraction times multiplication by scalars scalar product vectorial product inverse exponentiation Functions length dimensions transpose linear independence rank determinant minor

Arithmetic operations with vectors and matrices (addition, subtraction and multiplication) are denoted by the usual symbols of WIRIS.

plus:  command +

Vector or matrix addition. Operands must be of the same type and have the same dimensions.

subtraction:  command -

Operands must be of the same type and have the same dimensions.

times:  command * or ·

Product of matrices or scalar product of vectors.

The number of columns in the first operand must be the same as the number of rows in the second. In WIRIS, all vectors are row vectors, but this is not a restriction. In order to multiply a matrix by a row vector, the vector is considered as a column vector as long as this permits multiplying.

The symbol * always appears as · in accordance with typographical convention.

multiplication by scalars:  command * or ·

Product of a vector or matrix by a scalar.

The symbol, * , always appears as · in accordance with typographical convention.

scalar product:  Icon , command * or ·

Scalar product of two vectors of the same length.

The symbol * always appears as · in accordance with typographical convention.

vectorial product:  Icon , command vectorial_product

Cross product of two vectors.

The cross product is defined for two vectors of length 3.

inverse:  Icon , command inverse

Inverse matrix.

If the matrix can be inverted, its inverse is returned.. If the matrix cannot be inverted, an error is returned.

exponentiation:  Icon , command ^

A square matrix can be raised to a whole number power. If we raise it to a negative power and the matrix can be inverted, the inverse of the matrix is raised to the absolute value of the exponent. If the matrix cannot be inverted, an error is returned.

length:  command length

If applied to a vector, the number of components is obtained; if applied to a matrix, the number of rows is obtained.

dimensions:  command dimensions

WIRIS returns the sequence formed by the number of rows and the number of columns in a matrix, respectively.

transpose:  Icon , command transpose or '

WIRIS returns the transpose of the original matrix.

linear independence:  command linearly_independents?

Given two or more vectors of the same length, the following is obtained: true if they are linearly independent and false if they are not.

rank:  command rank

Calculates the rank of a matrix.

determinant:  Icon or , command determinant

Given a square matrix, this calculates its determinant.

minor:  command minor

Given a square matrix, A and two integers i and j, this calculates the minor corresponding to the position Aij of the matrix. This minor is the determinant of the matrix obtained by eliminating, from A the row i and the column j.