Schur Decomposition
From the book
Chapter 9: Matrix Decompositions and Beyond. In the chapter mind map this icon labels Schur Decomp: $A = QTQ^\top$. The discussion below is excerpted and lightly edited from § Theorem: Schur Decomposition in Mathematics for AI and Machine Learning.
For any square matrix $A \in \mathbb{R}^{N \times N}$, there exists an orthonormal matrix $Q \in \mathbb{R}^{N \times N}$ and an upper triangular matrix $U \in \mathbb{R}^{N \times N}$ such that
What this drawing shows
What you see. Represents triangularization by a unitary or orthogonal change of basis.
In the mind map. Chapter 9 — Schur Decomp. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 9: Matrix Decompositions and Beyond — see the mind-map node Schur Decomp.