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Chapter 8: Q3E (page 411)

Let be an orthogonal n脳nmatrix. Find the singular values of A algebraically.

Short Answer

Expert verified

The singular values of A are 蟽i=1=1fori=1,2,..n.

Step by step solution

01

of 2: Given information

It is given that, A is an orthogonal n脳nmatrix.

02

of 2: Find the singular value

Let us find the singular values of A by computing the eigen values of the square matrix A'A.

As A is an orthogonal n脳n matrix, therefore A'A=ln.

This implies that the eigenvalues of A'Aare 位1=1fori=1,2,..n

Hence the singular values of A are 蟽i=1=1fori=1,2,..n

Result:When is an orthogonal matrix, the singular values of A are 蟽i=1=1fori=1,2,..n

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