Linear Algebra/Notation

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Linear Algebra
 ← Cover Notation Introduction → 


, , real numbers, reals greater than , ordered -tuples of reals

natural numbers:

complex numbers

set of . . . such that . . .


interval (open or closed) of reals between and

sequence; like a set but order matters

vector spaces



zero vector, zero vector of


standard basis for

basis vectors

matrix representing the vector

set of -th degree polynomials

set of matrices

span of the set

direct sum of subspaces

isomorphic spaces

homomorphisms, linear maps


transformations; maps from a space to itself

square matrices

matrix representing the map

matrix entry from row , column

determinant of the matrix

rangespace and nullspace of the map

generalized rangespace and nullspace

Lower case Greek alphabet[edit]

About the Cover. This is Cramer's Rule for the system , . The size of the first box is the determinant shown (the absolute value of the size is the area). The size of the second box is times that, and equals the size of the final box. Hence, is the final determinant divided by the first determinant.

Linear Algebra
 ← Cover Notation Introduction →