Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Square Matrix

Chapter 2 Linear algebra

Chapter 2: Matrix — Square

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

From the book

Chapter 2: Matrix. In the chapter mind map this icon labels Square. The discussion below is excerpted and lightly edited from § Theorem: Left Inverse Equals Right Inverse for Square Matrices in Mathematics for AI and Machine Learning.

Let $A \in \mathbb{R}^{N \times N}$. If there exists a matrix $B \in \mathbb{R}^{N \times N}$ such that $AB = I_{N \times N}$, then $A$ is invertible, $B = A^{-1}$, and consequently $BA = I_{N \times N}$.

In particular, for any invertible matrix $A$, $AA^{-1} = A^{-1}A = I_{N \times N}$.

What this drawing shows

What you see. Matrix with the same number of rows and columns, representing endomorphisms and eigenvalue problems.

In the mind map. Chapter 2 — Square. See From the book above for definitions, figures, and worked examples.

Where to read next

Open Chapter 2 companion →

Read the full definitions, figures, and worked examples in Chapter 2: Matrix — see the mind-map node Square.