Scalars
Arithmetic on single numbers and the field axioms they obey. Numbers may be integers, decimals, fractions (1/2), pi or sqrt(2).
Vectors
Components, norms, unit vectors and direction angles. Numbers may be integers, decimals, fractions (1/2), pi or sqrt(2).
Vector operations
Addition, scaling, linear combinations, distance and projection. Numbers may be integers, decimals, fractions (1/2), pi or sqrt(2).
Dot products
Inner product, angle, orthogonality, projection and inequalities. Numbers may be integers, decimals, fractions (1/2), pi or sqrt(2).
Cross products
u × v, areas, normals, and scalar / vector triple products. Numbers may be integers, decimals, fractions (1/2), pi or sqrt(2).
Vector spaces
Axioms, span membership, fundamental subspaces and subspace tests. Numbers may be integers, decimals, fractions (1/2), pi or sqrt(2).
Linear independence
Independence test, dependency relations and Gram matrix. Numbers may be integers, decimals, fractions (1/2), pi or sqrt(2).
Basis & dimension
Basis of a span, coordinates, extension and Gram–Schmidt. Numbers may be integers, decimals, fractions (1/2), pi or sqrt(2).