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Vectors · Linear Algebra | Math Infinitum

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Linear Algebra
Vectors

Linear Algebra · Chapter 01

Vectors

Direction and magnitude. One idea, two ways to see it.

Connect a geometric arrow to a pair of numbers. This first chapter begins with the meaning of a vector in the plane.

v = x e_{1} + y e_{2}

(x y)

u + v

∥ v ∥ = x^{2} + y^{2}

c v

e_{1}, e_{2}

R^{2}

P Q

Lessons

Build the foundation

01What Is a Vector?See how an arrow, a displacement, and a pair of coordinates describe the same idea.Read lesson →
02What the coordinates scaleA pair of coordinates is not a pair of labels. It is a pair of instructions: stretch this arrow by so much, stretch that one by so much, and add whatever you get.Read lesson →