Dear Forumers.
I am working on the following problem.
Let matrix P=( A B ) where A and B are matrices. Let P be an n*n orthogonal matrix.
Show that A'A is an idempotent matrix.
I do not know where to start. Thanks in advance for the help.
Thanks for the help.
There is a problem with the dimensions.
X is n*k
because each of X1,..,Xk is n*1
So I was going to write (using your help)
X(X'X)^{-1}X'= X(X^{-1}X'^{-1})X'
But X^{-1} does not exist
Hi everyone,
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...
I understand the lines you wrote. But I do not know where to take it from here.
What should I do with
LaTeX Code: X(X^{-1}Xsingle-quote^{-1})Xsingle-quote
?
Thanks a lot for the help.
Hi everyone,
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...
Hi everyone,
I would need to get some help on the following question
Let A (m*n)
Let B (m*p)
Let L(A) be the span of the columns of A.
L(A) is orthogonal to L(B) <=> A'B=0
I suppose that the => direction is pretty obvious, since A is in L(A)
and B in is L(B).
Now I am not sure how to...
Here is the example I found
A1=
1,0,0;
0,0,0;
1,0,0;
A2=
0,0,0;
0,1,0;
0,0,0;
A1+A2=
1,0,0;
0,1,0;
1,0,0;
All three are idempotent. Is there a way to make those matrices a little less trivial.