Matrix Transforms: nxm, n->m, m->n, n+m->n/m

In summary, a matrix of dimension nxm can perform various transformations, such as transforming a vector of dimension n to a vector of dimension m, or vice versa. It can also transform a larger vector of dimension n+m to a smaller vector of dimension m or n. Matrix multiplication is used to perform these transformations.
  • #1
Imiebee
1
0
A matrix of dimension nxm
a. transforms a vector of dimension n to a vector of dimension m
b. transforms a vector of dimension m to a vector of dimension n
c. a vector of dimension n+m to a vector of dimension m
d. a vector of dimension n+m to a vector of dimension n
 
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  • #2
Matrix multiplication (note that a vector is just an m x 1 matrix)

(n x m) X (m x k) => (n x k)

See if you can figure it out now.
 
  • #3
Please use a meaningful title. Please don't just "dump" your problem on us. Please show some effort so that the helpers who are helping voluntarily will actually want to help.
 
  • #4
Imiebee said:
A matrix of dimension nxm
So which is the number of rows and which is the number of columns?

a. transforms a vector of dimension n to a vector of dimension m
b. transforms a vector of dimension m to a vector of dimension n
c. a vector of dimension n+m to a vector of dimension m
d. a vector of dimension n+m to a vector of dimension n
 

FAQ: Matrix Transforms: nxm, n->m, m->n, n+m->n/m

1. What are matrix transforms?

Matrix transforms are mathematical operations that involve transforming a matrix from one form to another. This can include changing the dimensions of the matrix, converting between row and column vectors, or performing operations on the elements of the matrix.

2. What is the difference between nxm and n->m?

Nxm refers to the dimensions of a matrix, where n represents the number of rows and m represents the number of columns. On the other hand, n->m represents a transformation from a matrix with n rows to a matrix with m rows. This transformation can involve changing the dimensions, rearranging the elements, or performing operations on the matrix.

3. How is m->n different from n->m?

M->n and n->m are both matrix transformations, but they involve different changes to the matrix. M->n involves transforming a matrix with m rows to a matrix with n rows, while n->m involves transforming a matrix with n rows to a matrix with m rows. This can result in different dimensions and arrangements of the elements in the matrix.

4. What does n+m->n/m mean?

N+m->n/m is a matrix transformation that involves adding two matrices together and then transforming the resulting matrix. The "n/m" at the end indicates that the resulting matrix will have n rows and m columns. This transformation can involve changing the dimensions, rearranging the elements, or performing operations on the matrix.

5. How are matrix transforms used in science?

Matrix transforms are used in a variety of scientific fields, including physics, engineering, and computer science. They are used to represent and manipulate data, perform calculations, and model complex systems. Some common applications include image processing, data analysis, and simulation of physical systems.

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