Posted by **Lisa** on Wednesday, September 8, 2010 at 4:18am.

For a given square matrix A the predicted values of matrix B are:

predicted B=A(A'A)^(-1)A'B

why is the matrix C=A(A'A)^(-1)A' an idempotent and symmetric matrix? and is this matrix invertible?

- MATHS----Matrix -
**MathMate**, Wednesday, September 8, 2010 at 11:26am
Assuming (A'A) is invertible, then (A'A)^{-1} exists.

A(A'A)^{-1}A'

By the property of inverse of product of matrices,

(A'A)^{-1}

=A^{-1} A'^{-1}

Therefore

C=A(A'A)^{-1}A'

=A(A^{-1} A'^{-1})A'

=(A A^{-1}) (A'^{-1}A')

= (I) (I)

=I

after application of associativity and the properties of inverse of matrices.

Since I is idempotent and invertible, so is C.

- Equation of parabola -
**Bayarbold**, Friday, June 10, 2011 at 11:10am
The equation of the parabola which contains 2 points (1,1) and (-2,-2) and whose tangent at the point (1,1) has the slope k is y=1/3(A)x^2+1/3(B)x-2/3(C) Express A,B and C with k.Please solve this problem.please

## Answer This Question

## Related Questions

- Math - Hi! I need help with these two questions. Thanks! :) 1.) Can we multiply ...
- linear algebra - 1)If A is an invertible matrix and k is a positive integer, ...
- Math - Mark each of the following True or False. ___ a. All vectors in an ...
- science - 1 A ……... is a rectangular array of numbers that are ...
- Matrix - Let A be an invertible n x n matrix, and let B be an n x p matrix. ...
- linear algebra - 3. Suppose A is symmetric positive definite and Q is an ...
- math - This is a matrix question. R is the matrix (3r 1) (s 2s) 1. State, in ...
- math - This is a matrix question. R is the matrix (3r 1) (s 2s) 1. State, in ...
- Math - Fine the size of the following matrix and its additive inverse matrix. ...
- algebra - Hi guys: Can any one please tell me what does this means? Thanks...

More Related Questions