Question

Linear Algebra: Please explain what happened between the first and second steps?

Let a be a scalar. Let x, y, and z be vectors.
x^T * y = (a(y/||y||) + z)^T * y
= a||y||

Answer 1

Is (a(y/||y||) the scalar a times y divided by the magnitude of y?

Answer 2

yes sir

Answer 3

and x to the T is the transform of x?

Answer 4

sorry for the late reply, but it's meant to be the transpose of the vector x