Question

Let W be a linear space with an inner product and
A : W → W be a linear map whose image is one dimensional (so in the case of matrices,
it has rank one). Let ~v 6= 0 be an in the image of A, so it is a basis for the image. If
h~v, (I + A)~vi 6= 0, show that I + A is invertible by finding a formula for the inverse.

Answer 1

didn't write it properly

Answer 2

What is ~v 6 = 0?

Answer 3

Okay, I'll work on it once you repost!