Asking about matrix division

In summary, the conversation discusses two different ways to write the matrix division operation, which involves finding the solution to the equation XB=A or BX=A. This can be solved using Gaussian elimination as long as the matrix B is not singular. However, if B is singular, the pseudo-inverse must be used to find the solution. The purpose of matrix division is to find the solution to equations involving matrices, and it can be useful in various applications such as solving systems of linear equations and performing transformations in linear algebra.
  • #1
Sledge
1
0
Is it possible to compute matrix (A/B) without first finding the inverse of matrix B but ending with EITHER { A * (Inverse of B) } OR { (Inverse of B * A }...i think i discovered the trick
 
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  • #2
Another way to write ##X=A/B \equiv AB^{-1}## is ##XB=A##. This has a unique solution X if B is not singular. You can solve for X in XB=A using Gaussian elimination.

Another way to write ##X=B \backslash A \equiv B^{-1}A## is ##BX=A##. This, too, has a a unique solution X if B is not singular. You can solve for X in BX=A using Gaussian elimination.

What if B is singular? The standard approach is to use the pseudo-inverse, and now you have but no choice to compute that inverse, typically via singular value decomposition.
 
  • #3
what would be the uses of matrix division?
 

1. What is matrix division?

Matrix division is a mathematical operation used to divide one matrix by another. It is similar to regular division, but instead of dividing numbers, we divide matrices.

2. How is matrix division different from regular division?

Matrix division is different from regular division because it involves dividing two matrices together, while regular division involves dividing two numbers. In matrix division, the size and shape of the matrices must also match in order for the division to be possible.

3. What are the requirements for matrix division?

The two matrices being divided must have the same number of columns and rows in order for the division to be possible. Additionally, the divisor matrix cannot have any zero values in order to avoid undefined results.

4. What is the result of matrix division?

The result of matrix division is a new matrix that is the product of the dividend and the inverse of the divisor. This new matrix will have the same number of rows as the dividend and the same number of columns as the divisor.

5. Are there any special cases in matrix division?

Yes, there are two special cases in matrix division. The first is when the divisor matrix is a scalar, meaning it is a single value and not a matrix. In this case, the scalar value is divided into each element of the dividend matrix. The second special case is when the divisor matrix is a square matrix and the dividend matrix is the identity matrix, resulting in the inverse of the divisor matrix.

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