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# N-dimensional space

Select from the following:
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.

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