Pathway XII

⟨,⟩Inner products and operators

Length and angle from a pairing. Orthogonal projection is the closest point.

1. 01Inner productsAn inner product gives lengths and angles. The projection of v onto u is the closest point on that line.4 min
2. 02The spectral theoremA symmetric matrix is an orthogonal stretch: eigenvectors are the axes, eigenvalues the stretch factors.4 min