Significance of Singular Values

This matlab code is intended to demonstrate the interpretation of the singular values

Description

This program is made by Md. Iftekhar Tanveer ([e-mail])

 This matlab code is intended to demonstrate the physical significance/interpretation of the elements of diagonal matrix in Singular Value Decomposition (SVD).
 
Here, multiple rows of a BIG matrix is gradually being filled with 'ones' which means the information content is being reduced. Now, the eigenvalues and their 1st and 2nd derivatives are plotted.

From the plot is can be seen that the number of eigenvalues with high values have a strong relationship with information content in the matrix.

This measurement is accurate even when the matrix is non-singular. The stability of this measurement can be checked by incorporating some noise as done in 'option 1' of the code.

• MATLAB release: MATLAB 7.8 (R2009a)