Matrix condition number question

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SUMMARY

The discussion centers on the applicability of condition numbers to non-square matrices, specifically in the context of MATLAB's capabilities. While the traditional definition of condition number, defined as cond(A) = ||A||.||A^-1||, applies to square matrices, MATLAB can compute condition numbers for non-square matrices. This is significant as it indicates that condition numbers can provide insights into rank deficiency in least squares analysis, despite the absence of an inverse for non-square matrices.

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tim51
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Hey,

I've been studying condition numbers for matrices. I found a past exam question that asks if the notion of condition numbers can be used for non-square matrices.

Intuitively I thought it couldn't because cond(A) = ||A||.||A^-1|| and non-square matrices have no inverse. But MATLAB will calculate it?

Why do condition numbers exist for non-square matricies and do they have any meaning at all?

Thanks.
 
Physics news on Phys.org
Least squares analysis involves non-square matrices and condition number is a meaure of rank deficiency.
 

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