ABSTRACT
Unitary transformations preserve the inner product. Hence, they preserve the metric quantities that stem from the inner product, such as length, distance, and angle. While a general similarity preserves the algebraic features of a linear transformation, such as the characteristic and minimal polynomials, the rank, and the Jordan canonical form, unitary similarities also preserve metric features such as the norm, singular values, and the numerical range. Unitary similarities are desirable in computational linear algebra for stability reasons.
