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linalg::det -- determinant of a matrix

Introduction

linalg::det(A) computes the determinant of the square matrix A.

Call(s)

linalg::det(A)

Parameters

A - a square matrix of a domain of category Cat::Matrix.

Returns

an element of the component ring of A.

Related Functions

linalg::gaussElim, linalg::permanent, linalg::rank, numeric::det

Details

Example 1

We compute the determinant of the following matrix:

>> A := matrix([[a11, a12], [a21, a22]])
                              +-          -+
                              |  a11, a12  |
                              |            |
                              |  a21, a22  |
                              +-          -+

which gives us the well-known formula for the determinant of an arbitrary 2x2 matrix:

>> linalg::det(A)
                             a11 a22 - a12 a21

Background

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