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

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SUMMARY

The discussion focuses on matrix transformations involving dimensions nxm, where a matrix can transform vectors between different dimensions. Specifically, it outlines how a matrix of dimension nxm can transform a vector of dimension n to dimension m, a vector of dimension m to dimension n, and vectors of dimension n+m to both dimensions n and m. The mathematical representation of matrix multiplication is also highlighted, confirming that the product of an nxm matrix and an mxk matrix results in an nxk matrix.

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  • Familiarity with vector transformations
  • Knowledge of matrix multiplication rules
  • Basic linear algebra concepts
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Imiebee
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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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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.
 
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.
 
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
 

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