# Compact notation for block diagonal matrices?

Is there a more compact notation for representing a block-diagonal matrix than

$\left[\begin{array}{cccc} \mathbf{W}_1 & 0 & ... & 0\\ 0 & \mathbf{W}_2 & ... & 0\\ 0 & 0 & \ddots & 0\\ 0 & 0 & ... & \mathbf{W}_n \end{array}\right]$

Something as simple as replacing

$\left[\begin{array}{c} \mathbf{m}_1\\ \mathbf{m}_2\\ \vdots\\ \mathbf{m}_n \end{array}\right]$

with

$\left[\mathbf{m}_1^T~\mathbf{m}_2^T~...~\mathbf{m}_n^T\right]^T$

for vectors? I'm just trying to reduce the space required for a manuscript. Is

$diag\left\{\mathbf{W}_1~ \mathbf{W}_2~...~\mathbf{W}_n \right\}$

acceptable notation?

• As long as you explain what you mean, you can use any notation you like. The "diag" notation looks perfectly fine to me. – Hans Lundmark Dec 30 '14 at 15:26
• Using the kronecker product you can write your matrix as $\sum_{i=1}^ke_ie_i^t\otimes W_i$ and your vector as $\sum_{i=1}^ke_i\otimes m_i$, where $e_1,\ldots,e_k$ is the canonical basis of $\mathbb{F}^k$. – Daniel Dec 30 '14 at 15:42
• Both of these are good options and answer the question. Never would have occurred to me to use a kronecker product. Thank you. – Andy K. Dec 31 '14 at 16:16
• I've seen blkdiag(...) in papers – Nick Alger Apr 8 '17 at 3:07

$\text{blkdiag} \left( \left\{ \mathbf{W}_i \right\}_{i=1}^n \right)$