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 \({\bf A}^{-1}\)?