MATLAB Mathematics - SERC - Index of

1 Matrices and Linear Algebra
Inverses and Determinants
This section provides
• An overview of the use of inverses and determinants for solving square
nonsingular systems of linear equations
• A discussion of the Moore-Penrose pseudoinverse for solving rectangular
systems of linear equations
Overview
If A is square and nonsingular, the equations AX = I and XA = I have the same
solution, X. This solution is called the inverse of A, is denoted by A -1 , and is
computed by the function inv. The determinant of a matrix is useful in
theoretical considerations and some types of symbolic computation, but its
scaling and roundoff error properties make it far less satisfactory for numeric
computation. Nevertheless, the function det computes the determinant of a
square matrix:
A = pascal(3)
A =
1 1 1
1 2 3
1 3 6
d = det(A)
X = inv(A)
d =
X =
1
3 -3 1
-3 5 -2
1 -2 1
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