Who first did use the symbol $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ for a matrix and similarly $\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$?
Why do these two conventions exist independently to the present day?

Were whenever efforts made to unify the symbols?

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    $\begingroup$ See Earliest Uses of Symbols for Matrices and Vectors. $\endgroup$ – Mauro ALLEGRANZA Jan 31 '18 at 13:50
  • $\begingroup$ @MauroALLEGRANZA Thank you for the link, it gives some insight into problem but it doesn't clarify it in reference to two most used symbols nowadays. $\endgroup$ – Widawensen Jan 31 '18 at 14:02
  • $\begingroup$ In "A Memoir ..", as I see the symbol is very close however a little different.. entries are additionally separated with commas.. to the second book it seems I have no access.. $\endgroup$ – Widawensen Jan 31 '18 at 14:26
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    $\begingroup$ @MauroALLEGRANZA I've read the "A memoir ..." in one breath, it is wonderful, delicious.. I'm very grateful for providing this particular link.. Cayley surprisingly was using the symbol which is a mix of two modernly used symbols.. thank you also for telling about Cullis, who did popularize "rounded parenthesis" ? we still don't know , do you know why some people use the first symbol, others the second one ? It depends on country ? why there is no unification ? Maybe some interesting story is behind all of this.. (BTW - you said so much that you could consider also to give it as an answer ) $\endgroup$ – Widawensen Feb 1 '18 at 13:20

See Earliest Uses of Symbols for Matrices and Vectors.

The first similar symbol seems to be the "mixed" one used by Cayley into his “A Memoir on the Theory of Matrices” (1858).

A following reference is M.Bocher, Introduction to Higher Algebra (1907), page 20-21.

The "squared parenthesis" notation is due to Cullis, Matrices and Determinoids, 1st ed. 1913.

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  • $\begingroup$ Finally I've downloaded also Boucher's book. He used double vertical lines for matrices at his book, although he mentioned also about rounded parentheses.. very interesting.. $\endgroup$ – Widawensen Feb 1 '18 at 13:57

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