Is there any difference in mathematical notations between French and English? I studied Mathematics mainly in French and now I am going to write research articles in English. I would like to know if there are some important differences in mathematical notations between French and English. 
For instance, I noticed that the decimal mark in English is a dot (.) whereas in French it is a comma (,).
 A: I think you know this one already, the open/closed intervals:
$\underset{\text{french}}{]a,b]} = \underset{\text{english}}{(a,b]}$ e.t.c.
Then as far as I know Corps (could be translated as Field) in French is usually not necessarily commutative, while the english expression Field always requires commutativity.
These are just two things I noticed, but I think that is already all I know, neither french nor english is my native language.
A: Note: these are general differences; sometimes a french author might use an English notation for any reason whatsoever.
This list obviously does not apply when a French mathematician writes something in English, in which case they will use English conventions.
Numbers
The decimal separator in French is the comma $,$. The thousands separator in French is the space.
$\underset{\text{English}}{1,\!345.67} = \underset{\text{French}}{1~345,\!67}$
Tuples, vectors, coordinates
The semi-colon $;$ is sometimes used in tuple-like structures instead of the comma $,$ in cases where the comma could be mistaken for the decimal separator (or because of personal preference).
$\underset{\text{English}}{(1,2,3)} = \underset{\text{French}}{(1;2;3)}$
Intervals
An open interval is denoted with an open square bracket, instead of a parenthesis:
$\underset{\text{English}}{[a,+\infty)} = \underset{\text{French}}{[a,+\infty[}$
$\underset{\text{English}}{(-\infty,+\infty)} = \underset{\text{French}}{]-\infty,+\infty[}$
Integer intervals
I'm not sure if this notation is used in English mathematics, but in any case the French one seems fairly common in French literature. The English notation is completely understood for a French person.
$\underset{\text{English}}{\{3, \dots, 42\}} = \underset{\text{French}}{[\![3,42]\!]}$
These brackets are basically to $[~]$ what $\mathbb{N}$ is to $N$.
In LaTeX you would use \llbracket and \rrbracket from package stmaryrd; this is not available in MathJax.
Cross product (vector product)
Cross product (called "produit vectoriel" (vector product) in French) uses the wedge symbol $\wedge$ instead of the typical mutliplication cross symbol $\times$.
$\underset{\text{English}}{\vec{a} \times \vec{b}} = \underset{\text{French}}{\vec{a} \wedge \vec{b}}$
Scalar triple product (mixed product)
This one is anecdotal. There seems to be multiple notations used for that in France, including the English one.
$\underset{\text{English}}{[\vec{a},\vec{b},\vec{c}]} = \underset{\text{French}}{(\!(\vec{a},\vec{b},\vec{c})\!)}$
Sets
In French mathematics, $0$ is both positive and negative. Therefore, we always have:
$\underset{\text{French}}{\mathbb{N}} = \underset{\text{French}}{\mathbb{Z}_+} = \underset{\text{English}}{[0, +\infty)}$
To omit the $0$ in these sets, one adds a superscript star $*$:
$\underset{\text{English}}{\mathbb{N}} = \underset{\text{French}}{\mathbb{N}^*}$
Function names
Both English and traditional French names are used in French mathematics since they don't lead to any confusions.
$\underset{\text{English}}{cosh} = \underset{\text{French}}{ch}$
$\underset{\text{English}}{sinh} = \underset{\text{French}}{sh}$
$\underset{\text{English}}{tanh} = \underset{\text{French}}{th}$
$\underset{\text{English}}{arcosh} = \underset{\text{French}}{argch}$
$\underset{\text{English}}{arsinh} = \underset{\text{French}}{argsh}$
$\underset{\text{English}}{artanh} = \underset{\text{French}}{argth}$
Transposition
Traditionally, the French notation for transposition is a preceeding superscript $t$, instead of a following superscript $\intercal$. The English notation is sometimes used, notably in Computer Science circles.
$\underset{\text{English}}{M^\intercal} = \underset{\text{French}}{^t\!M}$
Note that one has to remove the extra space after the preceeding superscript in the French notation, using \! in LaTeX/MathJax.
Integral evaluation
$\displaystyle\int_a^b x^2\;\mathrm{d}x = \underset{\text{English}}{\tfrac{1}{3} x^3 \Big|_a^b} = \underset{\text{French}}{\Big[\tfrac{1}{3} x^3 \Big]_a^b}$
The English notation is sometimes used.
Binomial coefficient (n choose k)
$\underset{\text{English}}{n \choose k} = \underset{\text{French}}{C^k_n}$
The $C$ stands for "combinaison" (combination).
Note that the $k$ is on top and the $n$ on the bottom in the French notation.
The English notation is pretty much standard in French mathematics nowadays.
A: In traditional French typography for maths, uppercase letters and Greek letters should be upright. 
Some functions names were different tg and cotg for tan and cot, sh, ch and th for sinh, cosh and tanh. The inverse trigonometric functions had an initial capital (Arcsin, instead of arcsin). The inverse hyperbolic functions are (were?)  denoted argsh, argch, argth, instead of arsinh, arcosh, artanh.
In linear algebra, the transpose of a matrix is usually denoted with a prescript roman t: ${}^{\mathrm t\!}A$.
A: I have seen $\mathrm{Vect}(u_1, u_2, u_3)$ used to denote a linear subspace of $V$ generated by the vectors $u_1, u_2, u_3 \in V$, which I would normally write as $\langle u_1, u_2, u_3\rangle$.
I don't know how common $\mathrm{Vect}$ is used but here are some examples where I've seen it:

*

*https://math.unice.fr/~ah/ens/cours/alg10/sousesp.pdf

*https://fr.wikipedia.org/w/index.php?title=Sous-espace_vectoriel_engendr%C3%A9&oldid=178218559
