Linear Algebra

Matrix Condition Number

low condition number -> matrix is well conditioned
high condition number -> matrix is ill conditioned

infinity -> matrix is singular (non-invertible)

A matrix that is not invertible has a condition number of infinity.

What does this mean in a practical sense? When using the formula \( \textbf{Ax = b} \), a matrix \( \textbf{A} \) with a high condition number is usually unsuitable when solving real-world problems, as it means that a small change in \(b\) will result in a large change in \(\textbf{x}\).