2007-5.md

course	course_year	question_number	tags	title	year
Linear Algebra	IB	5	IB 2007 Linear Algebra	4.I.1G	2007

Suppose that $\alpha: V \rightarrow W$ is a linear map of finite-dimensional complex vector spaces. What is the dual map $\alpha^{*}$ of the dual vector spaces?

Suppose that we choose bases of $V, W$ and take the corresponding dual bases of the dual vector spaces. What is the relation between the matrices that represent $\alpha$ and $\alpha^{*}$ with respect to these bases? Justify your answer.