The Power of Orthogonal Matrices

Some matrices have a secret superpower: finding their inverse is as easy as flipping them.

These are called orthogonal matrices. Their columns are made of special vectors that are

all perpendicular to each other and have a length of one. Think of them as

the perfect, non-squishy building blocks of a transformation. Because of this neat trick,

multiplying the matrix by its flipped version (the transpose) gives you the identity matrix.

This is a massive shortcut that makes solving huge, messy systems of equations in machine

learning way simpler and more stable. It's a cheat code for complex math.