Definition:Congruence
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Congruence may refer to:
- Geometry:
- Congruence: Two geometric figures are congruent if they are both "the same size and shape".
- Metric Spaces:
- Congruence (Metric Spaces): Two subsets of a space are congruent if there exists an isometry between them.
- Abstract Algebra:
- Congruence Modulo an Ideal: A concept in ideal theory.
- Congruence Relation: An equivalence on an algebraic structure which is compatible with its operation.
- Number Theory:
- Congruence (Number Theory): Two real numbers $x$ and $y$ are congruent (modulo $z \in \R$) if and only if $x \bmod z = y \bmod z$
- Linear Algebra:
- Matrix Congruence: $\mathbf A$ and $\mathbf B$ are congruent if and only if there exists an invertible matrix $\mathbf P$ such that $\mathbf B = \mathbf P^\intercal \mathbf A \mathbf P$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): congruence: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): congruence: 1.