Math Is Fun Forum

mathacc

Guest

Matrix X'X=A is given <- how to get X?

Sry too simple question probably.
But I have the matrix X'X (=A) given, and have to find X. X is symmetric. Is there an easy trick? thanks

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Matrix X'X=A is given <- how to get X?

What is X′? Is it the transpose of X? If it is, then you should know that if X is symmetric, its transpose is equal to X itself.

mathacc

Guest

Re: Matrix X'X=A is given <- how to get X?

hi yes thats clear.
X' is the transpose of X.
but (X'X) is given. how to get the single X or X', respectively?

thanks

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Matrix X'X=A is given <- how to get X?

What’s the size of X? If X is only 2×2, you can let

and try and solve for X. If X is a bigger matrix, well … it’s a bit more complicated.

mathacc

Guest

Re: Matrix X'X=A is given <- how to get X?

it's actually a 4x4 matrix

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Matrix X'X=A is given <- how to get X?

What's A? It's a hard problem to solve in general, but if A is nice we might have some shortcuts.
Especially if it's got a lot of 0's.

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Why did the vector cross the road?
It wanted to be normal.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Matrix X'X=A is given <- how to get X?

I guess you should take primary manipulation both horizontally and vertically until you reduce it to simple I matrix, that is
A=P[sub]n[/sub]...P[sub]3[/sub]P[sub]2[/sub]P[sub]1[/sub]IP'[sub]1[/sub]P'[sub]2[/sub]P'[sub]3[/sub]...P'[sub]n[/sub]

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X'(y-Xβ)=0