#matrices
15. Linear and Multilinear Algebra; Matrix Theory
This volume develops vector spaces, linear maps, matrices, and multilinear structures. It serves as a core toolkit for nearly all areas of mathematics, physics, and computation. Part I. Vector Spaces Chapter 1. Vector Spaces 1.1 Definitions and examples 1.2 Subspaces 1.3 Linear combinations 1.4 Span and generation 1.5 Linear independence Chapter 2. Bases and Dimension 2.1 Bases 2.2 Existence of bases 2.3 Dimension 2.4 Coordinate representations 2.5 Change of basis...
Tiling
Array Tiling Array tiling divides a multidimensional array into small rectangular regions called tiles. Each tile is processed before moving to the next tile. You use it when matrix or grid operations touch nearby elements repeatedly and cache locality affects performance. Problem Given a matrix $A$ with $r$ rows and $c$ columns, process all elements in tiles of size: $$ t_r \times t_c $$ where $t_r$ is the tile height...