Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: 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
xi	The i-th element of vector x
cij	The element in matrix C at row i and column j
x1 ... xn	Elements from x1 to xn
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
AX is congruent to B	AX is congruent to B
ak	a raised to the k power
ex	Exponential function of x
AT; xT	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 xi, where: The complex conjugate of the complex matrix element cjk
xH; AH	The complex conjugate transpose of vector x; the complex conjugate transpose of matrix A
	The sum of elements x1 to xn
	The square root of a+b
	The integral from a to b of f(x) dx
||x||2	The Euclidean norm of vector x, defined as:
||A||1	The one norm of matrix A, defined as:
||A||2	The spectral norm of matrix A, defined as: max{||Ax||2 : ||x||2 = 1}
||A||F	The Frobenius norm of matrix A, defined as:
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
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
int(x)	The largest integer that is less than or equal to x
x mod(m)	x modulo m; the remainder when x is divided by m
infinity	Infinity
pi	Pi, 3.14159265...