Matrix proof help PLZ!

outermeasure · **Posted:** Sat, 1 Oct 2011 10:39:00 UTC

twinwings wrote:

I think...dimensions of Px=nxn and Px=I (I still have some trouble with this)

No!

need not be the identity matrix.

We know X^TX

is invertible k-by-k, hence $\mathop{\mathrm{rank}}X\geq k$ , hence $n\geq k$ . If $X=\begin{pmatrix}I_{k\times k}\\0_{(n-k)\times k}\end{pmatrix}$ , then $X^TX=I_{k\times k}$ , so $P_X=X(X^TX)^{-1}X^T=XX^T=\begin{pmatrix}I_{k\times k} & 0_{k\times(n-k)}\\0_{(n-k)\times k} & 0_{(n-k)\times(n-k)}\end{pmatrix}$ .

chrisdelp · **Joined:** Mon, 3 Oct 2011 03:54:01 UTC **Posts:** 1

Hey guys, i was just wondering if anyone could shed some light on part (c)? I understand the previous 2 parts, but part (c) has me really lost for ideas. Thanks a ton.

outermeasure · **Posted:** Mon, 3 Oct 2011 10:03:38 UTC

chrisdelp wrote:

Hey guys, i was just wondering if anyone could shed some light on part (c)? I understand the previous 2 parts, but part (c) has me really lost for ideas. Thanks a ton.

Just calculate $P_Y=Y(Y^TY)^{-1}Y^T$ when Y=XA

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Matrix proof help PLZ!

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