Linear Algebra

Caution

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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 $\textbf{x}$.