# How to represent a tensor/matrix/vector/array in blackboard? [closed]

While teaching in the blackboard, I find it difficult to represent a vector/matrix/tensor. In latex, we represent $\mathbf{x}$. But, how do we represent it while writing in chalk? Is it okay to write an underlined variable $\underline{x}$ instead? What is the usual practice?

I think, avoiding the bold text might confuse the students.

## closed as off-topic by padawan, user3209815, Buzz, Cape Code, CoderNov 1 '17 at 17:08

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• I think this question is more appropriate for math.SE. Also, on that site LaTeX is enabled so what you have written will make more sense. – David Ketcheson Nov 1 '17 at 7:21
• Probably worth checking matheducators.SE to see if this has been asked before. – astronat Nov 1 '17 at 7:31
• I find it amusing that questions are now being asked "how to write on a chalkboard" :) – Solar Mike Nov 1 '17 at 9:05
• For what is worth, there is even an ISO standard that says you can use $\vec{v}$ instead: en.wikipedia.org/wiki/ISO_31-11#Vectors_and_tensors. – Federico Poloni Nov 1 '17 at 9:37
• The first question to ask when migrating is, "is this question off-topic here?" The answer here is no, this is very relevant to Academia. The fact is may fit elsewhere also doesn't make it off-topic here. I think this should stay. – eykanal Nov 1 '17 at 14:47

The following are the notations I've seen most along the years (I don't think there's a winner).

Vectors:

Matrices:

In my experience, unadorned symbols are preferred by mathematicians; the arrow is preferred by physicists; and bar and underbar (and double underbar for matrices) are preferred by engineers.

Even though I don't have to write many vectors and matrices (in my classes I deal mainly with scalar quantities), I usually employ underbarred symbols for four reasons:

1. Of course, I'm an engineer!
2. A bar is faster to draw then an arrow.
3. My handwriting is awful, and I think that simpler symbols improve readability; at the same time, though, I don't want to abandon the categorization of quantities through different symbols.
4. The interpretation of underbar is frequently that of bold, and I prefer bold symbols for vectors over symbols with an arrow.
• Don't you think, a student might get confused with upper-bar{x}, considering it as a compliment. I used lower-bar{x} today. – Coder Nov 1 '17 at 17:14
• @Coder Yes, the upper bar is used for the logical complement and, sometimes, for the complex conjugate. However, you frequently don't have all these elements in the same course, and for the complex conjugate one can use a star. When I was a student, I simply copied the notation used by the professor, without adapting it to my preferences. – Massimo Ortolano Nov 1 '17 at 17:19
• I agree. yes it is highly unlikely that all these will come in the same course. Thanks. – Coder Nov 1 '17 at 17:34
• The barred vector looks more like an average than a vector. While a vector usually has a one-sided arrow, a tensor usually has a double-sided arrow, and a matrix has a pointed hat. (... at least in my experience as a physics student.) – MPath Nov 1 '17 at 18:39

That very field dependent (and probably also depends on country, city, course,…). Here's my answer:

• For mathematicians, I do not make any distinction, but follow the convention that vectors get lower case letters, while matrices are upper case. Some mathematicians get get confused for a few weeks, but get used to it pretty quick.

• For physicists, I sometimes use $\vec x$ for vectors and upper case for matrices. Usually that is fine, but note that the word "vector" has a different meaning in physics, than in math. If $\vec x$ is too complicated for you, you could also use $\bar x$ or $\underline x$ for vectors. For engineers, I would probably do the same.

• If I would teach tensor calculus, I would probably use one underline for vectors two for matrices and three for three-tensors. (But I never did teach this, so I can not confirm if this is really practical…). Another possibility for tensor calculus is to write $(a_{ijk})$ for a three tensor (similarly $(x_k)$ is a vector $(a_{ij})$ is a matrix and $(a_{i_1,i_2,\dots, i_k})$ is k-tensor.

• There's really no difference in the modern definitions of vectors and tensors in physics and mathematics. There was such a difference 50 or more years ago, but not really today. – Massimo Ortolano Nov 2 '17 at 12:55
• @MassimoOrtolano Oh, that's interesting. I remember that my physics prof told us in the late 90s that a vector is a "triplet that transforms like space" (I never got what that meant, though). An example was that the triplet (temperature, pressure, x-coordinate) is not a vector in the physical sense… – Dirk Nov 2 '17 at 13:04
• Yes, that's the old point of view, which was actually already surpassed in the late '90s. I'm a bit in hurry now, but if you wish I can come back later on this, maybe in chat. Or the next time I come to Braunschweig (I happen to go at PTB there sometimes) :-) – Massimo Ortolano Nov 2 '17 at 13:37
• So, yes, in the olden times physicists defined vectors and tensors as array of number which transformed in two possible ways under changes of the coordinate system. An example of such a definition can be found in this book, p. 27 (pdf) from 1943. It's in Italian, but I think that the different mathematical approach with respect to modern books is evident. – Massimo Ortolano Nov 2 '17 at 18:10
• Learned something new today, thanks! In case you're in Braunschweig, give me a ping! – Dirk Nov 2 '17 at 18:24

This might depend on your country and subject.

In Germany vectors are usually written as $\vec{x}$ (i.e. with an arrow above the letter), matrices and tensors as capital letters. It has been done like this in all school classes I've ever attended and in most university lectures. If I remember correctly, some professors used underlining for matrices instead (not sure about vectors, perhaps also underlining).

As long as you use a consistent representation it shouldn't be a problem for the students. But the best approach might be to just ask them what they are used to. You could also get the information about what is usual in your place/subject by asking other teachers, looking at lecture notes or sample solutions for exercises and tests, etc.

Another common convention (at least in my field) is :

• Uppercase for matrices: $A$, $B$, $C$.
• Lowercase for vectors: $v$, $w$.
• Greek lowercase for scalars: $\alpha$, $\lambda$.
• Sometimes, calligraphic for tensors (as in: things with three or more indices): $\mathcal{A}$.

If you use this convention, there is no need for bold/italic/bars/arrows.