# On Algebra

# Table of Contents

# Essence of Linear Algebra

Let us talk about the essence of Linear Algebra.

## Span and Basis

Span $=$ defined by all vectors that can be represented as a linear combination of the given vectors.

Basis of a space $=$ linearly independent vectors that span the entire given space.

## Dot Product

Dot product $=$ duality of a linear transformation (use for projections).