Guide and Reference

Special Characters, Symbols, Expressions, and Abbreviations

The mathematical and programming notations used in this book are consistent with traditional mathematical and programming usage. These conventions are explained below, along with special abbreviations that are associated with specific values.

Item Description
Greek letters: alpha, sigma, omega, OMEGA Symbolic scalar values
|a| The absolute value of a
a*b The dot product of a and b
x_i The i-th element of vector x
c_ij The element in matrix C at row i and column j
x₁ ... x_n Elements from x₁ to x_n
i = 1, n i is assigned the values 1 to n
y <-- x Vector y is replaced by vector x
xy Vector x times vector y
a^k a raised to the k power
e^x Exponential function of x
A^T; x^T The transpose of matrix A; the transpose of vector x

The complex conjugate of vector x; the complex conjugate of matrix A

The complex conjugate of the complex vector element x_i, where:

The complex conjugate of the complex matrix element c_jk
x^H; A^H The complex conjugate transpose of vector x; the complex conjugate transpose of matrix A
I Identity matrix

The sum of elements x₁ to x_n

The square root of a+b

A^-1
The inverse of matrix A

A^-T
The transpose of A inverse
|A| The determinant of matrix A
m by n matrix A Matrix A has m rows and n columns
sin a The sine of a
cos b The cosine of b
SIGN (a) The sign of a; the result is either + or -
address {a} The storage address of a
size(a, dim) The result equals the number of elements in a along a specified dimension dim or if dim is not present the total number of array elements in a.
max(x) The maximum element in vector x
min(x) The minimum element in vector x
ceiling(x) The smallest integer that is greater than or equal to x
floor(x) The largest integer that is not greater than x
iceil(m,n) The smallest integer that is greater than or equal to m/n; that is, iceil(m,n) = ceiling(m/n)
int(x), x > 0 The largest integer that is less than or equal to x
m --> (p, i) m is mapped into (p, i)
mod(x, m) x modulo m; the remainder when x is divided by m
infinity Infinity
pi Pi, 3.14159265

Item	Description
Greek letters: alpha, sigma, omega, OMEGA	Symbolic scalar values
\|`a`\|	The absolute value of `a`
a*b	The dot product of a and b
`x`_i	The `i`-th element of vector x
`c`_ij	The element in matrix C at row `i` and column `j`
`x`₁ ... `x`_n	Elements from `x`₁ to `x`_n
`i` = 1, `n`	`i` is assigned the values 1 to `n`
y <-- x	Vector y is replaced by vector x
xy	Vector x times vector y
`a`^k	`a` raised to the `k` power
`e`^x	Exponential function of x
A^T; x^T	The transpose of matrix A; the transpose of vector x
	The complex conjugate of vector x; the complex conjugate of matrix A
	The complex conjugate of the complex vector element `x`_i, where: The complex conjugate of the complex matrix element `c`_jk
x^H; A^H	The complex conjugate transpose of vector x; the complex conjugate transpose of matrix A
`I`	Identity matrix
	The sum of elements `x`₁ to `x`_n
	The square root of `a`+`b`
A^-1	The inverse of matrix A
A^-T	The transpose of A inverse
\|A\|	The determinant of matrix A
`m` by `n` matrix A	Matrix A has `m` rows and `n` columns
sin `a`	The sine of `a`
cos `b`	The cosine of `b`
SIGN (`a`)	The sign of `a`; the result is either + or -
address {`a`}	The storage address of `a`
size(`a`, `dim`)	The result equals the number of elements in `a` along a specified dimension `dim` or if `dim` is not present the total number of array elements in `a`.
max(x)	The maximum element in vector x
min(x)	The minimum element in vector x
ceiling(`x`)	The smallest integer that is greater than or equal to `x`
floor(`x`)	The largest integer that is not greater than `x`
iceil(`m`,`n`)	The smallest integer that is greater than or equal to `m`/`n`; that is, iceil(m,n) = ceiling(`m`/`n`)
int(`x`), `x` > 0	The largest integer that is less than or equal to `x`
`m` --> (`p`, `i`)	`m` is mapped into (`p`, `i`)
mod(`x`, `m`)	`x` modulo `m`; the remainder when `x` is divided by `m`
infinity	Infinity
pi	Pi, 3.14159265

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