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Answered question


If T : R n R m is a matrix transformation, does T</math depend on the dimensions of R? i.e., is T one-one if m > n, m = n, or n > m?
Also, say if T is one-one, does this mean it is a matrix transformation and hence a linear transformation?

Answer & Explanation

Monserrat Cole

Monserrat Cole

Beginner2022-07-08Added 12 answers

Any matrix transformation T : R n R m is a linear transformation (and vice versa once you've specified bases). If n > m, then T cannot be injective because there cannot be n linearly independent vectors in R m . Finally, if n = m or n < m, one can say nothing about injectivity without more information. For instance, for n = m you have the zero matrix transformation (not injective) and the identity matrix transformation.

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