R, R +, R n real numbers, positive reals, n-tuples of reals N, C natural numbers {0, 1, 2, . . .}, complex numbers (a .. b), [a .. b] open interval, closed interval h. . .i sequence (a list in which order matters) hi,j row i and column j entry of matrix H V, W, U vector spaces ~v, ~0, ~0V vector, zero vector, zero vector of a space V Pn, Mn×m space of degree n polynomials, n×m matrices [S] span of a set hB, Di, β, ~ ~δ basis, basis vectors En = h~e1, . . . , ~eni standard basis for R n V =∼ W isomorphic spaces M ⊕ N direct sum of subspaces h, g homomorphisms (linear maps) t, s transformations (linear maps from a space to itself) RepB(~v), RepB,D(h) representation of a vector, a map Zn×m or Z, In×n or I zero matrix, identity matrix |T| determinant of the matrix R(h), N (h) range space, null space of the map R∞(h), N∞(h) generalized range space and null space Greek letters with pronounciation character name character name α alpha AL-fuh ν nu NEW β beta BAY-tuh ξ, Ξ xi KSIGH γ, Γ gamma GAM-muh o omicron OM-uh-CRON δ, ∆ delta DEL-tuh π, Π pi PIE epsilon EP-suh-lon ρ rho ROW ζ zeta ZAY-tuh σ, Σ sigma SIG-muh η eta AY-tuh τ tau TOW (as in cow) θ, Θ theta THAY-tuh υ, Υ upsilon OOP-suh-LON ι iota eye-OH-tuh φ, Φ phi FEE, or FI (as in hi) κ kappa KAP-uh χ chi KI (as in hi) λ, Λ lambda LAM-duh ψ, Ψ psi SIGH, or PSIGH µ mu MEW ω, Ω omega oh-MAY-guh Capitals shown are the ones that differ from Roman capitals