0
$\begingroup$

Just trying to think if this is possible. What would a good example be if so?

To be a little more clear, if I have a linearly independent set of vectors $x_1, x_2, \ldots, x_k$, is there a linear mapping that will produce a linearly dependent set of output vectors?

  • 4
    Do you mean $\{A\vec{x}\}$ is linearly dependent? If so, the zero map would be a good example. If the preimage is a basis then any noninvertible map will do.2011-10-26

2 Answers 2