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Transpose a matrix whose elements are themselves matrices 
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#1
Nov2112, 09:07 AM

P: 4

If I have (for simplicity) a vector ( A, B) where A and B are matrices how does the transpose of this look, is it ( A^{T}, B^{T}) or
(A^{T} B^{T}) 


#2
Nov2112, 10:05 AM

P: 828

Think about what the dimension should be.



#3
Nov2112, 11:31 AM

P: 4

or
(A B) 


#4
Nov2112, 11:44 AM

P: 4

Transpose a matrix whose elements are themselves matrices
I know that the transpose of a 1x2 matrix should be a 2x1 matrix but I don't know whether the elements actually inside the matrix should be transposed once I make the matrix a 2x1. Thank you in advance for any help. 


#5
Nov2112, 01:54 PM

P: 15

From wikipedia:
A B (columns of A written as rows) 


#6
Nov2112, 06:01 PM

Emeritus
Sci Advisor
PF Gold
P: 9,415

$$\begin{pmatrix}A^T\\ B^T\end{pmatrix}.$$ If you instead interpret it as a 1×2 matrix whose elements are are 2×2 matrices, then the standard definition of "transpose" would of course just give you $$\begin{pmatrix}A\\ B\end{pmatrix}.$$ I think the former interpretation is far more useful, and I assume that to some authors, this is a reason to use a different definition of "transpose", so that you can think of (A B) as a 1×2 matrix, and still have its transpose be $$\begin{pmatrix}A^T\\ B^T\end{pmatrix}.$$ I don't see any reason to use a definition that makes ##\begin{pmatrix}A & B\end{pmatrix}^T=\begin{pmatrix}A^T & B^T\end{pmatrix}##. 


#7
Nov2112, 06:14 PM

P: 4




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