MATHEMATICS

# 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 $$\textbf{x}$$.