Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Change of basis matrices but I'm having trouble with this question due to its context.

Let $V$ be the vector space of polynomials of degree at most $2$ over $\mathbb{R}$. Let $\mathbf{e}_1$, $\mathbf{e}_2$, $\mathbf{e}_3$ and $\mathbf{e}'_1$,$\mathbf{e}'_2$,$\mathbf{e}'_3$ be the bases $1$, $x$, $x^2$ and $1$, $(1-x)$, $(1+x)^2$ of $V$.

Write down the change of basis matrices from basis $\mathbf{e}'_i$ to $\mathbf{e}_i$, and from $\mathbf{e}_i$ to $\mathbf{e}'_i$.

share|improve this question

1 Answer 1

To change from the $e_i'$ basis to the $e_i$ basis, just expand each $e_i'$ in terms of the $e_i$ basis, i.e., $e_i'=a_{1i}e_1+\cdots +a_{3i}e_3$, then the $i$th column of the change of basis matrix will be $(a_{1i},a_{2i},a_{3i})^T$.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.