matrixcentric

Matrixcentric is an adjective describing a perspective that places matrices at the center of consideration in mathematics, computing, and related fields. A matrixcentric viewpoint treats matrices as the primary carriers of linear structure, with many fundamental objects—linear transformations, systems of equations, and multilinear problems—expressed and manipulated via matrices. In linear algebra, this contrasts with a vector- or coordinate-centric style, where attention is focused on individual vectors and their components, while matrix-based methods reveal global structure and enable compact formulations.

In education, a matrixcentric approach may emphasize matrix representations, matrix operations, and decompositions from the outset, illustrating how complex problems reduce to matrix computations. In software and high-performance computing, matrixcentric design organizes data and algorithms around dense or sparse matrices, enabling batch processing and efficient use of cache and vectorized hardware. Standard linear algebra libraries (for example, BLAS/LAPACK families) embody a matrixcentric pattern, exposing APIs that operate on batches of matrices or large matrices rather than single vector operations.

The term is not a formal mathematical category but a descriptive stance used to compare paradigms, optimize performance, or guide pedagogy. Potential trade-offs include greater abstraction and initial complexity, balanced against expressive power and computational efficiency in matrix-heavy domains such as simulations, machine learning, and graphics.

See also: vector-centric, tensor, linear algebra, numerical linear algebra, matrix decomposition.

---