Thread Subject: condition number of a matrix

Hi, I am confused with a problem of condition number of a matrix. My problelm is as follows. First I need to solve the overdetermined equation. For example, Ax=b and A is the matrix of 100*5 and b is 100*1 vecter. In matlab, it is easy to compute x by command x = A\b. Now I change a litte of three numbers in the matrix A and then I use x_change = A_change\b. It turned out that the value of x_change is much far from the previous value of x. Thus, I compute the condition number of matrix and find it is extremely large. My question is here. Does the condition number just serve for square matrix or it is meaningless for a matrix of 100*5. Please give me a hand. Thanks.

"dai " <279711585@qq.com> wrote in message <h4uc42$6dm$1@fred.mathworks.com>...
> Hi, I am confused with a problem of condition number of a matrix. My problelm is as follows. First I need to solve the overdetermined equation. For example, Ax=b and A is the matrix of 100*5 and b is 100*1 vecter. In matlab, it is easy to compute x by command x = A\b. Now I change a litte of three numbers in the matrix A and then I use x_change = A_change\b. It turned out that the value of x_change is much far from the previous value of x. Thus, I compute the condition number of matrix and find it is extremely large. My question is here. Does the condition number just serve for square matrix or it is meaningless for a matrix of 100*5. Please give me a hand. Thanks.

Yes. the condition number applies to a non-square matrix as
well as a square one. A large condition number tells you that
your problem is singular or nearly so. A large condition number
tells you that any small perturbations in your problem may be
greatly magnified in the solution of a system that involves your
matrix.

In practice, this is apparently exactly what you have observed.

John