Questions about Singular Valued Composition (SVD) and vector subspace.   If the value of the determinant is 0, the inverse matrix cannot be obtained, so a similar inverse matrix is obtained using SVD and specific value decomposition. So we got eigenvalues and eigenvectors in this way. But I wonder why this result comes out when one of the two eigenvectors is the year of homogenous equation and the other is the base of the row space.   The subject is linear algebra.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
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Questions about Singular Valued Composition (SVD) and vector subspace.

 

If the value of the determinant is 0, the inverse matrix cannot be obtained, so a similar inverse matrix is obtained using SVD and specific value decomposition. So we got eigenvalues and eigenvectors in this way.

But I wonder why this result comes out when one of the two eigenvectors is the year of homogenous equation and the other is the base of the row space.

 

The subject is linear algebra.

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