# similarity transformation

- Also called homothetic transformation. a mapping of a set by which each element in the set is mapped into a positive constant multiple of itself, the same constant being used for all elements.
- an operation performed upon a square matrix that leaves invariant its characteristic polynomial, trace, and determinant. The transformation is obtained by multiplying the given matrix on one side by any nonsingular matrix and on the other by the inverse of that nonsingular matrix.

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