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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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.