%% Determine if Matrix Is Singular
% Examine why the determinant is not an accurate measure of singularity.
% Create a 10-by-10 matrix by multiplying an identity matrix, eye(10), by a small number.

A = eye(10)*0.0001;

% The matrix A has very small entries along the main diagonal. However, A is not singular, because it is a multiple of the identity matrix.
%
% Calculate the determinant of A.

d = det(A)

% The determinant is extremely small. A tolerance test of the form abs(det(A)) < tol is likely to flag this matrix as singular. Although the determinant of the matrix is close to zero, A is actually not ill conditioned. Therefore, A is not close to being singular. The determinant of a matrix can be arbitrarily close to zero without conveying information about singularity.
% To investigate if A is singular, use either the cond or rcond functions.
%
% Calculate the condition number of A.

c = cond(A)

% The result confirms that A is not ill conditioned.
% Copyright 2012 The MathWorks, Inc.