# Review Questions for Condition Numbers

- What is the definition of a condition number?
- What is the condition number of solving \({\bf A}\mathbf{x} = \mathbf{b}\)?
- What is the condition number of matrix-vector multiplication?
- Calculate the \(p\)-norm condition number of a matrix for a given \(p\).
- Do you want a small condition number or a large condition number?
- What is the condition number of an orthogonal matrix?
- If you have \(p\) accurate digits in \({\bf A}\) and \(\mathbf{b}\), how many accurate digits do you have in the solution of \({\bf A}\mathbf{x} = \mathbf{b}\) if the condition number of \({\bf A}\) is \(\kappa\)?
- When solving a linear system \({\bf A}\mathbf{x} = \mathbf{b}\), does a small residual guarantee an accurate result?
- Consider solving a linear system \({\bf A}\mathbf{x} = \mathbf{b}\). When does Gaussian elimination with partial pivoting produce a small residual?
- How does the condition number of a matrix \({\bf A}\) relate to the condition number of \({\bf A}^{-1}\)?