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 June 6th, 2013, 02:50 AM #1 Newbie   Joined: Jun 2013 Posts: 2 Thanks: 0 Matrix - problem Dear all, I have some problems with matrix calculations. I have equation X^T * X = A. Matrix X and A are symmetrical and they are 3 x 3. I know the matrix A. How to calculate matrix X from the equation X^T * X = A ??? Regards, Michal
 June 6th, 2013, 04:27 PM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Matrix - problem If X is symmetrical then X^T= X, so X^TX= X^2= A. Let $X= \begin{bmatrix}a &b=&c \\ b=&d=&e\\ c=&e=&f\end{bmatrix}=$ Then $X^TX= X^2= \begin{bmatrix}a^2+ b^2+ c^&ab+ bd+ ce=&ac+ be+ cf \\ ab+ bd+ ce=&b^2+ d^2+ e^2=&bc+ de+ ef \\ ac+ be+ cf=&bd+ de+ ef=&c^2+ e^2+ f^2\end{bmatrix}=$ So if A is given as, say, $\begin{bmatrix}p & q & r \\ q & s & t \\ r & t & u\end{bmatrix}$ We must have $a^2+ b^2+ c^2= p$, $ab+ bd+ ce= q$, $ac+ be+ cf= r$, $b^2+ d^2+ e^2= s$, $bc+ de+ ef= t$, $c^2+ e^2+ f^2= u$ Six quadratic equations to solve for a, b, c, d, e, f.
 June 11th, 2013, 02:23 AM #3 Newbie   Joined: Jun 2013 Posts: 2 Thanks: 0 Re: Matrix - problem Thanks for your response. Yes, I will have 6 quadratic equations to solve for a, b, c, d, e, f. I started to solve it, but it's not easy to solve such quadratic equations.

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