Orthogonality

Orthogonality is a generalization of perpendicularity.

Contents

Description

The notation for orthogonality is ⊥, as in a⃗ ⊥ b⃗.

In R³ space, a vector is orthogonal to a plane.

If two vectors are perpendicular, they must satisfy the Pythagorean theorem. It follows that the dot product must be 0.

a^Ta + b^Tb = (a+b)^T(a+b)

a^Ta + b^Tb = a^Ta + b^Tb + a^Tb + b^Ta

0 = a^Tb + b^Ta

0 = 2(a^Tb)

0 = a^Tb