Linear algebra is usually the fledgling mathematician’s first introduction
to the real world of mathematics. “What?” you say. You’re wondering
what in tarnation you’ve been doing up to this point if it wasn’t real mathematics.
After all, you started with counting real numbers as a toddler and
have worked your way through some really good stuff — probably even some
calculus.
I’m not trying to diminish your accomplishments up to this point, but you’ve
now ventured into that world of mathematics that sheds a new light on mathematical
structure. All the tried-and-true rules and principles of arithmetic
and algebra and trigonometry and geometry still apply, but linear algebra
looks at those rules, dissects them, and helps you see them in depth.
(Da “Linear algebra for dummies”).