Ufyukyu

0 $begingroup$ I am new to linear algebra, and I just wanted to doublecheck my understanding of the following: $T: R^n to R^m$ is a linear transformation. True or false? If $n>m$ , then $operatorname{Ker}T neq {0}$ . This statement is correct, because if $n>m$ , then per definition $T$ is not injective. If $T$ is not injective, then $ operatorname{Ker}Tneq {0}$ . Is my understanding correct? Thank you! linear-algebra linear-transformations share | cite | improve this question edited Jan 23 at 15:01 Bernard 122k 7 41 116 ...