- #1

- 18

- 0

I am working on the following problem.

Suppose the set of vectors X1,..,Xk is a basis for linear space V1.

Suppose the set of vectors Y1,..,Yk is also a basis for linear space

V1.

Clearly the linear space spanned by the Xs equals the linear space

spanned by the Ys.

Set

X=[X1: X2 :...: Xk]

Y=[Y1: Y2 :...: Yk]

Construct an algebraic argument to show that

X(X'X)^(-1)X'=Y(Y'Y)^(-1)Y'

This is the idea I have:

X=PYP^{-1}

where P changes the basis from Y to X.

Is this the right avenue?Thanks in advance.