Prerequisite · Matrix Algebra Foundations

Notation Reference

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Notation

This page collects the symbolic conventions used throughout the Matrix Algebra readings. Return here any time a symbol's meaning is unclear.

$\mathbb{R},\;\mathbb{R}^+,\;\mathbb{R}^n$	real numbers, positive reals, n-tuples of reals
$\mathbb{N},\;\mathbb{C}$	natural numbers $\{0,1,2,\ldots\}$ , complex numbers
$(a\,..\,b),\;[a\,..\,b]$	open interval, closed interval
$\langle\,\ldots\,\rangle$	sequence (a list in which order matters)
$h_{i,j}$	row i and column j entry of matrix H
$V,\;W,\;U$	vector spaces
$\vec{v},\;\vec{0},\;\vec{0}_V$	vector, zero vector, zero vector of a space V
$\mathcal{P}_n,\;\mathcal{M}_{n\times m}$	space of degree n polynomials, n×m matrices
$[S]$	span of a set
$\langle B,D\rangle,\;\vec{\beta},\;\vec{\delta}$	basis, basis vectors
$\mathcal{E}_n = \langle\vec{e}_1,\ldots,\vec{e}_n\rangle$	standard basis for $\mathbb{R}^n$
$V \cong W$	isomorphic spaces
$M \oplus N$	direct sum of subspaces
$h,\;g$	homomorphisms (linear maps between spaces)
$t,\;s$	transformations (linear maps from a space to itself)
$\mathrm{Rep}_B(\vec{v}),\;\mathrm{Rep}_{B,D}(h)$	representation of a vector, a map
$Z_{n\times m}$ or $Z$ , $\;I_{n\times n}$ or $I$	zero matrix, identity matrix
$\|T\|$	determinant of the matrix
$\mathcal{R}(h),\;\mathcal{N}(h)$	range space, null space of the map
$\mathcal{R}_\infty(h),\;\mathcal{N}_\infty(h)$	generalized range space and null space

character	name	character	name
$\alpha$	alpha AL-fuh	$\nu$	nu NEW
$\beta$	beta BAY-tuh	$\xi,\;\Xi$	xi KSIGH
$\gamma,\;\Gamma$	gamma GAM-muh	$o$	omicron OM-uh-CRON
$\delta,\;\Delta$	delta DEL-tuh	$\pi,\;\Pi$	pi PIE
$\epsilon$	epsilon EP-suh-lon	$\rho$	rho ROW
$\zeta$	zeta ZAY-tuh	$\sigma,\;\Sigma$	sigma SIG-muh
$\eta$	eta AY-tuh	$\tau$	tau TOW (as in cow)
$\theta,\;\Theta$	theta THAY-tuh	$\upsilon,\;\Upsilon$	upsilon OOP-suh-LON
$\iota$	iota eye-OH-tuh	$\phi,\;\Phi$	phi FEE, or FI (as in hi)
$\kappa$	kappa KAP-uh	$\chi$	chi KI (as in hi)
$\lambda,\;\Lambda$	lambda LAM-duh	$\psi,\;\Psi$	psi SIGH, or PSIGH
$\mu$	mu MEW	$\omega,\;\Omega$	omega oh-MAY-guh

Capitals shown are those that differ from Roman capitals.

References

Hefferon 2020 — Linear Algebra (Free textbook), jimhefferon.com/linearalgebra

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