Orthogonal Vectors: Vector Subspace and Dimension

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Covers linear independence, bases, and coordinate systems with examples and theorems.