Convention for symbol denoting a generic scalar quantity?

Question

Is there a convention for a symbol to denote any generic scalar?

Somehow I have in the back of my head that one would use $\lambda$ for that, but I cannot find any examples now.

Answer 1

There is no particular convention as far as I know. Many times I have found $\lambda$ and $\mu$, sometimes $a,b$ or $c$, etc. I think it really depends on the context, on which letters you have already used to denote other objects. The only recommendation is to be consistent: if you have started using lower case latin letters, do not switch to greek ones, or viceversa. Here is an example of what is better not to do. Suppose you have the following problem:

Let $(V,\langle \cdot, \cdot \rangle)$ be a vector space over $\mathbb{R}$ equipped with a bilinear form $\langle \cdot, \cdot \rangle$. Define $W=\{v \in V: \langle v, \cdot \rangle = 0\}$. Show that $W$ is a vector subspace of $V$.

Take $v,w \in W$ and $\lambda \in \mathbb{R}$. Then by bilinearity $\langle \lambda v+w,\cdot \rangle = \lambda\langle v,\cdot \rangle+\langle w, \cdot \rangle=0$. So we have shown that for each $a \in \mathbb{R}$ and $v,w \in W$, the vector $av+w$ sits in $W$, so $W$ is a vector space.

It is better to write instead for each $\lambda \in \mathbb{R}$ and $v,w \in W$, the vector $\lambda v+w$ sits in $W$, so $W$ is a vector space, keeping the same notations. However, I would not say it is a mistake to write $a v+w$ instead of $\lambda v+w$ once you have specified that $a \in \mathbb{R}$, because the meaning of the sentence is clear once you specifiy where all the objects live.

Answer 2

Yes, $\lambda$ is the most common, if you want to be specific that it is a scalar, you can write $\lambda \in \mathbb{F}$