Scalar when undefined: real, complex, or something else

107 Views Asked by At

For an arbitrary vector space one defines, the scalar field can be anything: real, complex, rational, or some other previously defined field.

However, in some texts on linear algebra for example, the authors do not define what a scalar is. Is it conventional to assume that, unless specified otherwise, a scalar is a real number? If not, in what topics, if any, is the conventional scalar taken to be complex numbers or some other field?

I realize this question may be somewhat fluffy, but I'd appreciate any inputs you may have.

1

There are 1 best solutions below

0
On

A scalar is simply an element of the field where the vector space is defined over.

It is usually understood what field you are working over.

So if V is a k-vector space, then a scalar is an element of k.