## Diagonalize a symmetric matrix associated to a form

Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.5 Solution: The matrix of $f$ in the standard basis is given by $\begin{pmatrix}1 & 2\\2& 4\end{pmatrix}$. Its eigenvalues are…

Write down a basis for the space of

a) $3\times 3$ symmetric matrices;

b) $n\times n$ symmetric matrices;

c) $n\times n$ anti-symmetric ($A^T = -A$) matrices; (more…)

Recall, that a matrix is called *symmetric* if $A^T = A$. Write down a basis in the space of *symmetric* $2\times 2$ matrices (there are many possible answers). How many elements are in the basis?

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