Linear Algebra

Notation
R real numbers
N natural numbers: {0, 1, 2,...}
C complex numbers
{... � � ...} set of ... such that ...
〈...〉 sequence; like a set but order matters
V,W,U vector spaces
�v, �w vectors
�0, �0V zero vector, zero vector of V
B,D bases
En = 〈�e1, ... , �en〉 standard basis for R n
�β, � δ basis vectors
Rep B(�v) matrix representing the vector
Pn set of n-th degree polynomials
Mn×m set of n×m matrices
[S] span of the set S
M ⊕ N direct sum of subspaces
V ∼ = W isomorphic spaces
h, g homomorphisms
H, G matrices
t, s transformations; maps from a space to itself
T,S square matrices
Rep B,D(h) matrix representing the map h
hi,j matrix entry from row i, column j
|T | determinant of the matrix T
R(h), N (h) rangespace and nullspace of the map h
R∞(h), N∞(h) generalized rangespace and nullspace
Lower case Greek alphabet
name symbol name symbol name symbol
alpha α iota ι rho ρ
beta β kappa κ sigma σ
gamma γ lambda λ tau τ
delta δ mu µ upsilon υ
epsilon ɛ nu ν phi φ
zeta ζ xi ξ chi χ
eta η omicron o psi ψ
theta θ pi π omega ω
Cover. This is Cramer’s Rule applied to the system x +2y =6,3x + y =8. Thearea
of the first box is the determinant shown. The area of the second box is x times that,
and equals the area of the final box. Hence, x is the final determinant divided by the
first determinant.