A matrix coefficient of a finite-dimensional group representation is a scalar function obtained by applying a linear functional to the translate of a fixed vector. In a chosen basis these functions include . For a finite group, the Schur orthogonality relations make the scaled coefficients of all inequivalent unitary irreducible representations an orthonormal basis of its scalar functions.
In the context of linear algebra and matrix theory, the term "matrix coefficient" can refer to a few different concepts depending on the specific area of study. Here are some possible interpretations: 1. **Matrix Elements**: In a square matrix, each entry or element is often referred to as a coefficient.
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