My Math Forum Transition matrix problem

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 August 25th, 2019, 10:43 AM #1 Member   Joined: Aug 2016 From: Romania Posts: 32 Thanks: 1 Transition matrix problem I have the following problem that asks me what is the transition matrix from B to B'.In the second image you can view the answer but I don't understand how that answer appeared. Can someone explain me the steps to solve this problem? I am also confused because the answer is a 3x3 matrix and all the matrices are in the form of a 2x2 which is not the same. https://ibb.co/YhSQ3Q1 https://ibb.co/y6DSrQf
 August 25th, 2019, 12:00 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,553 Thanks: 1403 $A$ is the solution to $B' = A^T B$ for example $\begin{pmatrix}1&0\\0&2\end{pmatrix} = \dfrac 1 2 \begin{pmatrix}2&0\\0&0\end{pmatrix}+ 0 \begin{pmatrix}0&3\\-3&0\end{pmatrix}+ \dfrac 2 5\begin{pmatrix}0&0\\0&5\end{pmatrix}$
August 25th, 2019, 12:38 PM   #3
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Quote:
 Originally Posted by romsek $A$ is the solution to $B' = A^T B$ for example $\begin{pmatrix}1&0\\0&2\end{pmatrix} = \dfrac 1 2 \begin{pmatrix}2&0\\0&0\end{pmatrix}+ 0 \begin{pmatrix}0&3\\-3&0\end{pmatrix}+ \dfrac 2 5\begin{pmatrix}0&0\\0&5\end{pmatrix}$
It will be something like this?
https://ibb.co/vxVtVCj

Also in your example A^(T) means a transposed matrix?

August 25th, 2019, 12:46 PM   #4
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Quote:
 Originally Posted by alex77 It will be something like this? https://ibb.co/vxVtVCj Also in your example A^(T) means a transposed matrix?
yes.

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