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I met a question when I tried to express a vector, where every element inside is a matrix. We know the notion usually works like this:

  • scalar: $a$
  • vector: $\boldsymbol{a}$
  • matrix: $\boldsymbol A$
  • vector (elements inside are vector): $\boldsymbol{A} = [\boldsymbol{a}_1, \boldsymbol{a} _2, \boldsymbol{a} _3]$

What if I want to express a vector (or tensor) where the elements are matrices, like the following:

  • vector (elements inside are vector): $? = [\boldsymbol{A}_1, \boldsymbol{A} _2, \boldsymbol{A} _3]$

Should I still use $\boldsymbol A$, Or is there a formal expression?

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This question is about conventions, and it will differ from field to field. You should use the conventions of your field.

Otherwise, the standard ISO 80000-2 identifies notation for scalars, vectors, matrices, tensors, and more. Symbols for tensors are in sans-serif bold italic. The isomath package implements this in LaTeX.

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  • $\begingroup$ Thank you so much for your answer, Arya! I checked the materials you mentioned, and it seems the symbols of matrix(2-15.1) and tensor(2-17.19) are the same: both are sans-serif bold italic with a capital case. Thanks again! $\endgroup$ – Nick Chen Jun 14 at 3:10
  • $\begingroup$ The matrix notation has serifs. The tensors don’t. $\endgroup$ – Arya McCarthy Jun 14 at 3:14
  • $\begingroup$ Sorry I didn't notice that difference! Thank you so much for pointing it out. Problem solved! $\endgroup$ – Nick Chen Jun 14 at 3:45
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    $\begingroup$ +1 for isomath, great little package $\endgroup$ – Firebug Jun 14 at 17:21

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