Linear Algebra

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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 \(\textbf{x}\).


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