- #1

TeenieBopper

- 29

- 0

This is for a regression analysis course, and I've only taken one introductory course on linear algebra, so when I Google'd "finding a symmetric matrix" a lot of stuff that I didn't understand came up.

## Homework Statement

Find the unique symmetric matrix A such that Y'AY=Y'GY

## Homework Equations

## The Attempt at a Solution

Y'AY = Y'GYY'AYY'=Y'GYY'

Y'AYY'(YY')^-1 = Y'GYY'(YY')^-1

Y'A=Y'G

YY'A=YY'G

(YY')^-1YY'A=YY')^-1YY'G

A=G

However, G is not symmetric:

G=

[1.0 1 1.0

-1.0 0 1.0

0.5 2 -0.5]

Other than the algebraic manipulation above, I don't know how else to approach this problem.