Inner Product

Jan 1, 2025 Linear Algebra 30 min read

Essence of Linear Algebra (1): The Essence of Vectors — More Than Just Arrows

Vectors are everywhere -- from GPS navigation to Netflix recommendations. This chapter builds your intuition from arrows in space to abstract vector spaces, covering addition, scalar multiplication, inner products, …

Oct 5, 2021 Functional Analysis 68 min read

Functional Analysis (3): Hilbert Spaces — Geometry in Infinite Dimensions

Inner products give infinite-dimensional spaces geometric structure — orthogonality, projections, and the Riesz representation theorem make Hilbert spaces the analyst's paradise.