Definition:Matrix/Indices

This page is about Index of Matrix Element. For other uses, see index.

Definition

Let $\mathbf A$ be an $m \times n$ matrix.

Let $a_{i j}$ be the element in row $i$ and column $j$ of $\mathbf A$.

Then the subscripts $i$ and $j$ are referred to as the indices (singular: index) of $a_{i j}$.

Linguistic Note

The plural of index is indices.

Compare vertex and apex, which have a similar plural form.

Sources

• 1954: A.C. Aitken: Determinants and Matrices (8th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions and Fundamental Operations of Matrices: $3$. The Notation of Matrices
• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 29$. Matrices
• 1980: A.J.M. Spencer: Continuum Mechanics ... (previous) ... (next): $2.1$: Matrices
• 1982: A.O. Morris: Linear Algebra: An Introduction (2nd ed.) ... (previous) ... (next): Chapter $1$: Linear Equations and Matrices: $1.2$ Elementary Row Operations on Matrices: Definition $1.1$