What do we mean by Orthogonality ?

[prgyn8]

What is Orthogonality? 🤔

In simple terms, orthogonality means perpendicularity.
Two vectors are said to be orthogonal if they meet at a right angle (90°).
In 2D, this is easy to visualize—like the x-axis and y-axis on a graph.

But orthogonality is not just about geometry.
Mathematically, two vectors u and v are orthogonal if their dot product is zero:

This idea extends to higher dimensions too—even when we cannot “see” the vectors, we can still test for orthogonality with the dot product.

Orthogonality is important because it gives us a way to build independent directions in space, helping in simplifying problems, designing algorithms, and performing decompositions like QR decomposition, LU Decomposition etc..