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Block diagonal matrix - Definition |
| Related Words: Axis, Band, Bar, Bend, Bias, Biased, Chord, Crossways, Dash, Diameter, Directrix, Edge |
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In mathematics, a block diagonal matrix is a block matrix which is a square matrix, and having main diagonal blocks square matrices, such that the off-diagonal blocks are zero matrices. A block diagonal matrix A has the form
- <math> \mathbf{A} = \begin{bmatrix} A_{1} & 0 & \cdots & 0 \\ 0 & A_{2} & \cdots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \cdots & A_{n}
\end{bmatrix}. <math>
where Ak is an square matrix. Note that any square matrix can be trivially considered as a block diagonal matrix, taking n=1.
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