Definition:Matrix Direct Sum
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Definition
Let $\mathbf A = \sqbrk a_{m n}$ and $\mathbf B = \sqbrk b_{p q}$ be matrices.
The matrix direct sum of $\mathbf A$ and $\mathbf B$ is denoted $\mathbf A \oplus \mathbf B$ and is defined as:
- $\mathbf A \oplus \mathbf B := \begin {bmatrix} \mathbf A & \mathbf 0 \\ \mathbf 0 & \mathbf B \end {bmatrix}$
where $\mathbf 0$ is a zero matrix, the upper-right $\mathbf 0$ being $m \times q$ and the lower left $\mathbf 0$ being $n \times p$.
Thus, if:
then $\mathbf A \oplus \mathbf B$ is a matrix with order $\paren {m + p} \times \paren {n + q}$.
Also see
- Definition:Matrix Addition, where can be found different operations on matrices also referred to as addition:
Sources
- This article incorporates material from Direct sum of matrices on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.