Thread: matrix trace and idempotent

X is an n x K non-singular full rank matrix where n > K

Is the result of this matrix operation an idempotent matrix? (It seems to be when I do it in stata.)

Given the properties below, I am told it is possible to express the trace of the matrix that results from the above operation in terms of n and K. But I have been unable to figure out how. Can someone give me a clue?





(where A,B, and C are non-singular square matrices)

Originally Posted by rainer

X is an n x K non-singular full rank matrix where n > K

Is the result of this matrix operation an idempotent matrix? (It seems to be when I do it in stata.)

Given the properties below, I am told it is possible to express the trace of the matrix that results from the above operation in terms of n and K. But I have been unable to figure out how. Can someone give me a clue?





(where A,B, and C are non-singular square matrices)

What is , for a square matrix??

Tonio

Originally Posted by tonio

What is , for a square matrix??

Tonio

But X is not square. It is n-by-K, where n>K.

Originally Posted by rainer

But X is not square. It is n-by-K, where n>K.

Whatever: what is , anyway?

Tonio

Originally Posted by tonio

Whatever: what is , anyway?

Tonio

is the transpose of .

yields a square matrix. I think that's part of the trick.