Is MATLAB a programming language? What makes a program a programming language?

Question

So, I've learn some programs in my collage. My major is mathematics so I have to learn programs like Wolfram Mathematica, Python, and MATLAB. I already know that Python is programming language. But, Are Wolfram Mathematica and MATLAB programming languages? Because they have syntax like programming language, have kind of data like integer, floating point, array, etc. But, on the other side, they have so many built-in function that make me wonder "are those just software to compute something?"

Answer 1

A programming language 
- has a specific syntax that can be used to produce various kinds of output.
- is either interpreted or compiled to machine language as instructions for a computer.
- used to create programs which implements algorithms. (Important! Compare why HTML and CSS are not programming languages)
- May actually be derived from earlier programming languages.

Both Wolfram and MATLAB are programming languages because they fulfill the above characteristics.