Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Block Matrix

Chapter 10 Linear algebra

Chapter 10: Matrix Block Partitioning — Block Partitioning (also appears in Ch. 5, Ch. 6)

High-resolution PNG
Block Matrix — high-resolution mind-map icon

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: Key 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).

For block matrix multiplication, the most important patterns are when both matrices are partitioned, enabling parallel computation and distributed processing.

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

Open Chapter 10 companion →

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).