DEFINITIONS YOU NEED TO KNOW FOR MATH 360
A binary operation on a set S
A subset is closed under a binary operation
A binary operation is associative
A binary operation is commutative
An identity element for a binary operation
The inverse of an element under a binary operation with identity
A vector space
Vector subtraction
A subspace of a vector space
A line in a vector space
A plane in a vector space
A homogeneous system of linear equations
The trivial solution to such a system
A linear combination of a set of vectors
The span of a set of vectors / the subspace spanned by a set of vectors
A set of vectors spans the vector space
A set of vectors is linearly independent
A set of vectors is linearly dependent
A basis of a vector space
The dimension of a vector space
The coordinates of a vector relative to a given basis
Euclidean space, Rn
M(m,n), F(X)
C(X),
D(X), D(n)(X), P(X), Pn(X)
An inner product
An inner product space
The norm of a vector in an inner product space
Two vectors are orthogonal
The angle between two vectors in an inner product space
The projection of one vector onto another
A unit vector
An orthogonal set of vectors
An orthonormal set of vectors
A linear transformation (function, map, operator)
The kernel and image of a linear transformation
The row space and column space of a matrix
The rank of a matrix
The rank and nullity of a linear transformation
An isomorphism and two vector spaces are isomorphic
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