Linear Algebra/Notation

Notation

$ℝ$, ${ℝ}^{+}$, ${ℝ}^n$	real numbers, reals greater than $0$, ordered $n$-tuples of reals
$\mathbb{N}$	natural numbers: $\{0,1,2,\dots \}$
$ℂ$	complex numbers
$\{\dots |\dots \}$	set of . . . such that . . .
$(a..b)$, $[a..b]$	interval (open or closed) of reals between $a$ and $b$
$⟨\dots ⟩$	sequence; like a set but order matters
$V,W,U$	vector spaces
$\overrightarrow{v},\overrightarrow{w}$	vectors
$\overrightarrow{0}$, ${\overrightarrow{0}}_V$	zero vector, zero vector of $V$
$B,D$	bases
${ℰ}_n=⟨{\overrightarrow{e}}_1,\dots ,{\overrightarrow{e}}_n⟩$	standard basis for ${ℝ}^n$
$\overrightarrow{\beta },\overrightarrow{\delta }$	basis vectors
${\mathrm{R}\mathrm{e}\mathrm{p}}_B(\overrightarrow{v})$	matrix representing the vector
${𝒫}_n$	set of $n$-th degree polynomials
${ℳ}_{n\times m}$	set of $n\times m$ matrices
$[S]$	span of the set $S$
$M\oplus N$	direct sum of subspaces
$V\cong W$	isomorphic spaces
$h,g$	homomorphisms, linear maps
$H,G$	matrices
$t,s$	transformations; maps from a space to itself
$T,S$	square matrices
${\mathrm{R}\mathrm{e}\mathrm{p}}_{B,D}(h)$	matrix representing the map $h$
$h_{i,j}$	matrix entry from row $i$, column $j$
$\left|T\right|$	determinant of the matrix $T$
$ℛ(h),𝒩(h)$	rangespace and nullspace of the map $h$
${ℛ}_{\mathrm{\infty }}(h),{𝒩}_{\mathrm{\infty }}(h)$	generalized rangespace and nullspace

Lower case Greek alphabet

About the Cover. This is Cramer's Rule for the system $x_1+2x_2=6$, $3x_1+x_2=8$. 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 $x_1$ times that, and equals the size of the final box. Hence, $x_1$ is the final determinant divided by the first determinant.