%% Find Condition of Identity Matrix
% Examine why the reciprocal condition number is a more accurate measure of singularity than the determinant.
% Create a 5-by-5 multiple of the identity matrix.

A = eye(5)*0.01;

% This matrix is full rank and has five equal singular values, which you can confirm by calculating svd(A).
%
% Calculate the determinant of A.

det(A)

% Although the determinant of the matrix is close to zero, A is actually very well conditioned and not close to being singular.
%
% Calculate the reciprocal condition number of A.

rcond(A)

% The matrix has a reciprocal condition number of 1 and is, therefore, very well conditioned. Use rcond(A) or cond(A) rather than det(A) to confirm singularity of a matrix.
% Copyright 2012 The MathWorks, Inc.