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August 25th, 2019, 10:43 AM   #1
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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
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August 25th, 2019, 12:00 PM   #2
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$A$ is the solution to

$B' = A^T B$

for example

$\begin{pmatrix}1&0\\0&2\end{pmatrix} =
\dfrac 1 2 \begin{pmatrix}2&0\\0&0\end{pmatrix}+
0 \begin{pmatrix}0&3\\-3&0\end{pmatrix}+
\dfrac 2 5\begin{pmatrix}0&0\\0&5\end{pmatrix}$
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August 25th, 2019, 12:38 PM   #3
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Quote:
Originally Posted by romsek View Post
$A$ 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?
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August 25th, 2019, 12:46 PM   #4
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Quote:
Originally Posted by alex77 View Post
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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