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

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.