Website owner:  James Miller

N-dimensional space

Preliminary definitions, conventions and notations. n-vectors, n-space, dot products, m-dot products

Vector spaces and subspaces, linearly dependent and independent sets of vectors, space spanned by a set of vectors, basis of a vector space, sum and intersection space of two vector spaces, coordinate systems in vector spaces, changes in coordinates due to change in basis

Vectors over real n-space, Inner products, Orthogonal vectors and spaces, Triangle Inequality, Schwarz Inequality, Gram-Schmidt orthogonalization process, Gramian Matrix

Vectors over complex n-space, Inner products, Orthogonal vectors, Triangle Inequality, Schwarz Inequality, Gram-Schmidt orthogonalization process, Gramian Matrix, Unitary matrix, Unitary transformation.

Vectors in n-dimensional space. Orthogonal vectors. Pythagorean theorem. Orthogonal and orthonormal bases.

Origin of the ideas of n-dimensional space. Development of the concepts of n-space.