Definition:Equality of Matrices

Definition

Let $\mathbf A$ and $\mathbf B$ be matrices over an underlying structure $R$.

Then $\mathbf A$ is equal to $\mathbf B$ if and only if:

$(1): \quad$ the order of $\mathbf A$ equals the order of $\mathbf B$: $m \times n$, say

$(2): \quad$ for all $i \in \set {1, 2, \ldots, m}$ and $j \in \set {1, 2, \ldots, n}$, we have that $a_{i j} = b_{i j}$.

Sources

• 1954: A.C. Aitken: Determinants and Matrices (8th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions and Fundamental Operations of Matrices: $4$. Matrices, Row Vectors, Column Vectors, Scalars