Main Diagonal

Tags: #◇CSMATH2 #◇Linear Algebra #◇Computational Mathematics #◇Matrices #◇Matrix Operations #◇Computer Science #◇Vector Spaces #◇Linear Transformations

◇Overview

Definition: If A=[aij] is a Square Matrix of order n, the entries aij where i=j are called the main diagonal entries of the matrix. These are a11...

◇Key Concepts

Definition Example

◇Details / Theory

Definition: If A=[aij] is a ◇Square Matrix of order n, the entries aij where i=j are called the main diagonal entries of the matrix. These are a11,a22,…,ann. (Handout 2, Page 2) Example: For A=[2103 −142−2 10530 0171], the main diagonal entries are 2, 4, 3, and 1. (Handout 2, Page 2, modified example value)
Personal Note: The main diagonal runs from the top-left corner to the bottom-right corner.

◇Common Pitfalls

The main diagonal only exists meaningfully in square matrices for some operations (trace, determinant), but any matrix has entries $a_{ii}$ . Diagonal entries are $a_{11}, a_{22}, \ldots, a_{kk}$ where $k = \min(m, n)$ .

◇Summary

TL;DR — The main diagonal consists of entries $a_{ii}$ . It determines the trace, and is central to diagonal, triangular, and identity matrices.

◇Links

Related: - ◇Square Matrix Source / Reference:

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Related Notes: ◇Matrix Multiplication, ◇Definition of a Matrix

MAIN DIAGONAL