What is the reason behind having Orthogonal PCA's?

orthogonal
pca

#1

In PCA, there is a condition that the second PCA describes as much variability in data as possible with the constraint that it should be orthogonal to the 1st PCA.

Why is the 90 degree angle used here?

Wanted to know the math behind this,so if somebody could help me please!


#2

Hi Shuvayan
I am not entirely confident, but more or less this is the reason. Eigen vectors are obtained by feeding in the corresponding Eigen values (denoted by lamba1, lamda2,…). These Eigen values are nothing but the solution to an equation. This leads me to believe that basically the dot product of the Eigen vectors = 0. This will happen when cosine of the angle between the two vectors is zero. Thats why 90 degrees.