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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?

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  • $\begingroup$ As long as you explain what you mean, you can use any notation you like. The "diag" notation looks perfectly fine to me. $\endgroup$ – Hans Lundmark Dec 30 '14 at 15:26
  • $\begingroup$ 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 $\mathbb{F}^k$. $\endgroup$ – Daniel Dec 30 '14 at 15:42
  • $\begingroup$ Both of these are good options and answer the question. Never would have occurred to me to use a kronecker product. Thank you. $\endgroup$ – Andy K. Dec 31 '14 at 16:16
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    $\begingroup$ I've seen blkdiag(...) in papers $\endgroup$ – Nick Alger Apr 8 '17 at 3:07
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$ \text{blkdiag} \left( \left\{ \mathbf{W}_i \right\}_{i=1}^n \right) $

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  • $\begingroup$ I'd love to see a reference for this. $\endgroup$ – Waldir Leoncio Feb 1 at 13:00
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    $\begingroup$ @WaldirLeoncio blkdiag function needs to be explained, although it seems clear in the naming. The curly braces is standard set notation. The indexing is common math notation. That's the nearest to a reference I can give :) $\endgroup$ – JStrahl Feb 2 at 21:32

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