- #1

tobor8man

- 2

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*Mathematical Physics*by Sadri Hassani. It defines a vector abstractly. I will repeat that definition here rather more informally.

There are these things called vectors,

**a**,

**b**,

**x**etc., that have these properties:

You can add them

**a**+

**b**=

**b**+

**a**

**a**+ (

**b**+

**c**) = (

**b**+

**a**) +

**c**

**a**+

**0**=

**a**,

**0**is the zero vector

**a**+ (-

**a**) =

**0**

You can multiply them by complex numbers (scalars) like c, d

c(d

**a**) = (cd)

**a**

1

**a**=

**a**

Multiplication involving vectors and scalars is distributive

c(

**a**+

**b**) = c

**a**+ c

**b**

(c + d)

**a**= c

**a**+ d

**a**

And that is it.

Given that definition, a scalar is a vector, a matrix is a vector, a tensor is a vector. Yes?

Mind you, I have also read that scalars and vectors are a kinds of tensors, of rank 0 and 1 respectively. True?

Am I confused? Should I be?