| SYMBOL |
MEANING OF SYMBOL |
| $\exists\,,\ \ \forall$ |
there exists, for all (for every) |
| $\subset\,,\ \ \subsetneq$ |
set containment, proper set containment |
| $(t,y)$ |
ordered pair (data point) |
| $\{(t_i,y_i)\}_{i=1}^{N\text{ or }\infty}$ |
data set |
| $(t_i)\,,\ \ (y_i)$ |
time list, list of data values |
|
$i\,,$
$j\,,$
$k\,,$
$m\,,$
$n\,,$
$M\,,$
$N$
|
integer variables |
| $i$ |
$i := \sqrt{-1}\,,$ in context |
| $\boldsymbol {\rm z} = (z_i)$ |
generic list |
| $:=\,,\ \mapsto$ |
equal, by definition; maps to |
| $f : {\oldstyle D}(f) \to B$ |
function notation |
|
$\Bbb R\,,$
$\Bbb Z\,,$
$\Bbb Z^+\,,$
$\Bbb Q\,,$
$\Bbb C$
|
important sets of numbers |
| $(a,b)\,,\ [a,b]\,,\ (a,b]$ |
interval notation |
| $f_e$ |
extension of a function to $\,\Bbb R$
|
| $\mu_{\boldsymbol {\rm y}}$ |
mean of a finite list
|
| ${^r}{\boldsymbol {\rm x}}$ |
notation for a $p$-cycle
|
| $\Bbb P$ |
set of all periods of a periodic function
|
| glb |
greatest lower bound
|
| $\bigstar$ |
material beyond assumed prerequisites
|
| lcm |
least common multiple
|
| $a|b$ |
$a\,$ divides $\,b$
|
| $I_n\,,\ 0_{m,n}$ |
$n\times n\,$ identity, $\,m \times n\,$ zero matrices
|
| $A\sin(\omega t + \phi)$ |
sinusoid
|
| $\omega\,,\ f$ |
radian and cyclic frequency
|
| $g(t_i^-)\,,\ g(t_i^+)$ |
one-sided limits
|
| $\int_P$ |
integral over any interval of length $\,P$
|
| ${\text{e}}^{it}$ |
complex exponential function
|
| $\text{Re}(z)\,,\ \text{Im}(z)$ |
real, imaginary parts of a complex number
|
| $E(C)\,,\ \mu_C$ |
expected value of $\,C$
|
| $\text{var}(C)\,,\ \sigma^2$ |
variance of $\,C$
|
| $\|x\|$ |
norm of $\,x$
|
| $\Bbb R^n$ |
Euclidean $n$-space
|
| ${\boldsymbol {\rm y}}^t\,,\ {\boldsymbol {\rm X}}^t$ |
transpose of vector, matrix
|
| sup |
supremum, least upper bound
|
| $\|A\|_2$ |
$2$-norm for matrices
|
| $\det A$ |
determinant of matrix $\,A$
|
| $\boldsymbol{\rm A}_{ij}$ |
matrix entry, $\,i^{\text{th}}\,$ row,
$\,j^{\text{th}}\,$ column
|
| $\langle \boldsymbol {\rm u}\,,\boldsymbol {\rm v}\rangle$ |
Euclidean inner product
|
| $\boldsymbol{f}(\boldsymbol{\rm T})$ |
vector-valued function of a vector variable
|
| $f_n$ |
filter value
|
| $(\ldots,y_{-1},\hat{y_0},y_1,\ldots)$ |
doubly infinite list with origin
|
| $H(\omega)\,,\ \tilde H(f)$ |
transfer functions
|