condition number for a matrix with a variable

Question

How would I go about calculating $cond(A)$ for

A= $\begin{bmatrix}1 & c\\c & 1\end{bmatrix}$, $|c|\neq 1$

Answer 1

Explicitly calculate the singular values as a function of $c$, then take the ratio of the largest and smallest singular values. This is as easy as finding the eigenvalues in this case because the matrix is symmetric. To check your work you should get $\frac{\max \{ |1+c|,|1-c| \}}{\min \{ |1+c|,|1-c| \}}$.