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…
Solution to Linear Algebra Done Wrong Exercise 1.2.4
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…)
Solution to Linear Algebra Done Wrong Exercise 1.2.3
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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