Exercise 2.6

Question

If $u$ and $v$ are $m$-vectors, the matrix $A = I+ uv^*$ is known as a rank-one perturbation of the identity. Show that if $A$ is nonsingular, then its inverse has the form $A^{-1} =I+ auv^*$ for some scalar $a$, and give an expression for $a$. For what $u$ and $v$ is $A$ singular? If it is singular, what is $null(A)$?

Desh Raj · Accepted Answer

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Exercise 2.6

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Exercise 2.6

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