DavidB
10-04-2010, 09:11 PM
Hello.
I have recently been testing an updated program for computing the eigenvalues and eigenvectors of real, square matrices. I am trying to test it with matrices for which not all eigenvalues can be found. I had assumed that any matrix with two identical columns and/or two identical rows would cause the program to fail. For example, given a 6 x 6 matrix with two identical rows, I had expected the program to compute five eigenvalues and five eigenvectors and output a message to the effect that not all eigenvalues/eigenvectors could be computed for this matrix.
However, the program did compute 6 eigenvalues and 6 eigenvectors without outputting any errors. So, either my assumption was incorrect, or the program is incorrect.
Am I incorrect in assuming that an N x N matrix with two or more identical rows will have N–1 (or fewer) eigenvalues and eigenvectors?
If so, what would cause the matrix to have N–1 (or fewer) eigenvalues and eigenvectors? Could you please supply one or more example matrices; I would like to thoroughly test out the program with data that will cause it to fail--I want to ensure that the program fails gracefully.
.
I have recently been testing an updated program for computing the eigenvalues and eigenvectors of real, square matrices. I am trying to test it with matrices for which not all eigenvalues can be found. I had assumed that any matrix with two identical columns and/or two identical rows would cause the program to fail. For example, given a 6 x 6 matrix with two identical rows, I had expected the program to compute five eigenvalues and five eigenvectors and output a message to the effect that not all eigenvalues/eigenvectors could be computed for this matrix.
However, the program did compute 6 eigenvalues and 6 eigenvectors without outputting any errors. So, either my assumption was incorrect, or the program is incorrect.
Am I incorrect in assuming that an N x N matrix with two or more identical rows will have N–1 (or fewer) eigenvalues and eigenvectors?
If so, what would cause the matrix to have N–1 (or fewer) eigenvalues and eigenvectors? Could you please supply one or more example matrices; I would like to thoroughly test out the program with data that will cause it to fail--I want to ensure that the program fails gracefully.
.