Quick matrix transpose proof help

In summary, to prove that the product B`A` is permitted when AB is permitted, we need to use the properties of matrices A and B. These properties include the fact that the transpose of A, denoted by A`, is equal to the matrix with its rows and columns swapped, and that the matrix product C is calculated by summing the products of the corresponding elements of A and B.
  • #1
bossman007
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Homework Statement



let transpose of A be noted by A`

Show that if the matrix product AB is permitted, then so is the product B`A`, where

B`A`=(AB)`

Homework Equations



[itex]C_{ij}=ƩA_{ik} B_{kj}[/itex] where summing from k=1 to m

[itex]A`_{ij} = A_{ji}[/itex]

The Attempt at a Solution



It wants me to use the relevant equations to prove this, but I am not sure where to start, seeing as the most I have done with matrices so far is add and multiply them
 
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  • #2
What properties of matrices A and B do you think are needed for the multiplication AB to be a permitted operation?
 

What is a matrix transpose?

A matrix transpose involves flipping the rows and columns of a matrix. This results in a new matrix with the rows becoming the columns and the columns becoming the rows.

Why is matrix transpose important?

Matrix transpose is important because it allows for efficient manipulation and calculation of matrices. It also has many applications in fields such as linear algebra, computer graphics, and data analysis.

How do you prove the quick matrix transpose algorithm?

The quick matrix transpose algorithm can be proven by showing that it results in the correct transposed matrix. This can be done by manually calculating the transposed matrix and comparing it to the result of the algorithm.

What are the steps of the quick matrix transpose algorithm?

The steps of the quick matrix transpose algorithm are as follows:

  1. Initialize a new matrix with the dimensions of the original matrix, but with the rows and columns switched.
  2. Loop through the rows and columns of the original matrix.
  3. For each element in the original matrix, place it in the corresponding position in the new matrix (e.g. the element at row i, column j in the original matrix would be placed at row j, column i in the new matrix).
  4. Return the new transposed matrix.

Can the quick matrix transpose algorithm handle non-square matrices?

Yes, the quick matrix transpose algorithm can handle non-square matrices. It will simply switch the rows and columns, regardless of the dimensions of the original matrix.

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