# How to read this matrix notation

Excuse me for this basic question, but when reading some mathematic books I have encountered the following matrix:

W = 2diag([1 1 0,01])


Could anybody explain to me how can I read this? Is it just a diagonal matrix multiplied by 2?

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In which book have you read? – lavkush Jul 3 '14 at 14:27
Actually it is PhD thesis of one of my lecturers (unfortunatelly not in English) and I am wondering what did he think about writing matrix this way. – Niemand Jul 3 '14 at 14:30
I am not sure, he may mean decimal by , this. – lavkush Jul 3 '14 at 14:34
Yup, sometimes I forget than in my country we use , instead of ., it's sick :(. – Niemand Jul 3 '14 at 15:02

My guess would be $\texttt{2diag([1 1 0,01])}=\begin{bmatrix}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 0,02 \end{bmatrix}.$

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Presumably the comma is then a decimal separator? – Théophile Jul 3 '14 at 14:32
@Théophile, Yes. – user35603 Jul 3 '14 at 14:33
I thought that it was more matlab-like style to separate rows, but you kind of opened my eyes. Thank you! – Niemand Jul 3 '14 at 14:35
Ahhhh! The different radix fooled me. – John Jul 3 '14 at 14:45
I was thinking "second diagonal", perhaps the antidiagonal or the diagonal right above or below the main diagonal. – user2357112 Jul 3 '14 at 15:44

The most reliable way could be to ask your lecturer, otherwise there could be a missing or extra multiplication by $2$.

The line

W = 2diag([1 1 0,01])


in the question has been typeset as it could be a code from the program. It is not clear whether this is deliberate or occasional, and whether this is exactly how it looks like in the thesis. Moreover, []-brackets inside ()-brackets strengthen the conjecture that it could be a code from the program. It seems quite viable that the program has a function 2diag (using a naming convention to put 2 instead of to) that takes a list (cf. [...] syntax) and creates a corresponding diagonal matrix of an appropriate dimension. This way, 2diag([1 1 0,01]) will create $3x3$ matrix with $1$, $1$ and $0,01$ on its main diagonal. However, if this notation actually means $$2\,\times\,\text{diag}\{1,1,0.01\}$$ then the diagonal of the resulting matrix will be $2$, $2$ and $0,02$. That's why one should be careful.

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There are languages where a number followed by identifier is parsed as number multiplied by that identifier, e.g. in Mathematica 2a would be equivalent to 2*a. – Ruslan Jul 3 '14 at 18:30
@Ruslan - thanks! This remark shows that there could be even more confusion if the formula is taken out of context. As for Mathematica, I presume in this case the 1st character of the identifier can not be a digit? – Alexander Konovalov Jul 3 '14 at 19:47
Yes, a digit can't start identifier name. Frankly, I don't even know what languages do allow this. – Ruslan Jul 3 '14 at 21:07
@Ruslan: for example, in GAP, an identifier may contain letters, digits, symbols _ and @, and must contain at least one non-digit, but the position of that is not specified; thus, 100x is a valid identifier in GAP - see here – Alexander Konovalov Jul 3 '14 at 21:34