Block Matrix
Chapter 10: Matrix Block Partitioning — Block Partitioning (also appears in Ch. 5, Ch. 6)
From the book
Chapter 10: Matrix Block Partitioning. In the chapter mind map this icon labels Block Partitioning: Transpose, Addition & Multiplication. The discussion below is excerpted and lightly edited from § Block Matrix Multiplication: Two Partitioning Patterns in Mathematics for AI and Machine Learning. Related material also appears in Chapter 5 (Leading Principal Minors (LU Existence Conditions)), Chapter 6 (Affine & Homog. Coords).
Two patterns of block matrix multiplication recur. With $2 \times 2$ blocks on both sides, @eq:block-matrix-multiplication reads
each block a row of blocks of $A$ times a column of blocks of $B$. Splitting $A$ only by rows and $B$ only by columns leaves a single product in every block:
What this drawing shows
What you see. Represents a matrix split into rectangular submatrices so algebra can be performed at the block level.
In the mind map. Chapter 10 — Block Partitioning: Transpose, Addition & Multiplication. See From the book above for definitions, figures, and worked examples.
Also appears in Ch. 5 (Leading Principal Minors (LU Existence Conditions)); Ch. 6 (Affine & Homog. Coords).
Where to read next
Read the full definitions, figures, and worked examples in Chapter 10: Matrix Block Partitioning — see the mind-map node Block Partitioning: Transpose, Addition & Multiplication.
This concept is also referenced in Chapter 5 (Leading Principal Minors (LU Existence Conditions)); Chapter 6 (Affine & Homog. Coords).
