Glossary of Mathematical Notations
"Math is like love -- a simple idea but it can get complicated."  - R. Drabek.

 Symbol Use Description Definition/Example º º Defined equal Defined to be equal to º º Abreviated notation Ñx ¦(x) º Ñ¦ » » Approximately equal = = Light-based Unit Equivalence (given c,h, and kB) ¥ ¥ Infinity Cardinality(Z) x-1 x-1 (1,1,...,1) [x-1]i=1 å åi=mn f(i) Sum from i=m to n of f(i) åi=13 i2=12+22+32 ò òabf(x) dx Integral from x=a to b f(x), LimN ® ¥ åi=0N-1 f(a+i(b-a)/N)(a-b)/N d/dx (d/dx)f(x) Derivative of f(x) (aka f '(x)) Limd ® 0 d-1(f(x+d)-f(x)) ' ¦'(x) Derivative of function Limd ® 0 (f(x+d)-f(x))/d [x| Highest integer not above x Max { z Î Z : z £ x } [-3.6| = -4 ; aka floor(x) Int(x) ?, ?xy,z Conditional y if x=0, z else. NB: differs from C definition ! Factorial n! = n(n-1)...1 4!=24 nCr Binomial coefficient n! / ((r!(n-r)!) Number of unordered r-selections from n Functions Sin() Sin(x) x-1 sin(x)     aka. sinc(x) or sine cardinal Tan() Tan(x) x-1 tanx ↑ x↑ Exponentiation ex = åi=0¥ i!-1 xi ↓ x↓ Logarithm ln(x) (base e) Vectors and Matrices Dim Dim(a) Dimension of a Dim((0,4,6)) = 3 | | |x| Absolute value of x |-5.4|=5.4 |a| Euclidean length of a Ö(åi=1Dim(a) ai2) |A| Determinant of a square matrix Si,j,..sei,j,..s a1,i a2,j... a_N,s T AT Transpose of matrix (aTi,j) where aTj,i=ai,j | |¥ |a|¥ Infinity norm Max{ |ai| : 1 £ i £ Dim(a) } | |+ |a|+ Vector trace åi=1Dim(a) |ai| ~ a~ Normalised vector a/|a| . a.b Scalar Vector "Dot" Product åi=1Dim(a) aibi × a×b Vector Vector "Cross" Product [a×b]i=åj k=1Dim(a) ei j kajbk º aºb Matrix Vector Product (aºb)i j = aibj Ä aÄb Skewed matrix Vector Product aÄb = a.bI - abT · a·b Coordinatewise product (a1,a2)·(b1,b2)=(a1b1,a2b2) * a*b Inversive product (a.b) / (|a||b|) qÐ qÐ(a,b) Subtended angle cos-1(a*b) Ñ Ñ f(x) Gradient (Ñ f(x))i = df/dxi Ð Ðxa ¦(x) Directed dervivative (Ñ * a)¦(x) ï ïf=0 Evaluated at ¦(x) ïx0 = ¦(x0) Complex Numbers ^ z^ Complex conjugate x-iy + |z|+ Complex modulus (zz^)½ = (x2+y2)½ Multivectors a i-vector component Ù aÙb Outer product (akÙbm = (ab) ¿ a¿b Contractive inner product ak¿bm = (ab) . a.b Semi-Symmetric inner product ak.bm = (ab)<|m-k|> m,k¹ 0 ; 0 else × a×b Commutator product ½(ab-ba) ~ a~b AntiCommutator product ½(ab+ba) * a*b Inversive product (a¿b) / (|a||b|) D aDb Delta Product (ab) ¨ a¨b Generic linear product Represents any one of Ù,¿,.,× or geometric products ¨+ a¨+b Forced Euclidean geometric product * a* Dual ai-1 # a# Main involution åi(-1)ia § a§ Reverse åi(-1)½ i(i-1)a © a© Clifford conjugation a§# § a§ Mitian conjugation e(p+1)..NaeN..(p+1) † a† Hermitian conjugation a§§# ~ a~ Normalised a/|a| or similar, according to context ¯ ¯b(a) Projection (a¿b)b-1 ^ ^b(a) Rejection a - ¯b(a) Î a Î b Contained within ¯b(a) = a È aÈb Join See text Ç aÇb Meet See text |A|s |a|s Self scale See text [-] ¦[-](a,b) Skewsymmetroll ¦[-](a,b) º ¦(a,b) - ¦(b,a) Ñ ¦Ñp(a) Differential ¦Ñp(a) º (a.Ñp)¦(p) D ¦Dp(a) Adjoint ¦Dp(a) º Ñp(a.¦(p)) Ä aÄb Lie product Ðab - Ðba [a,b,..,f] Algebra generated by {a,b,..,f} Sets   and Logic : Such that Î x Î X x is element of X 5 Î Primes È A È B Set union { x : x Î A OR  x Î B } Ç A Ç B Set intersection { x : x Î A AND x Î B } " " x Î X For all x in X " x Î { 1,2,3} : x < 4 \$ \$ x Î X There exists an x in X \$ x Î { 1,2,3} : x > 2 f Empty Set {} N Natural numbers { 1,2,3,...} Z Integers { 0,1,-1,2,-2,...} Z+ Nonnegative Integers { 0,1,2,...} ZN Nonnegative Integers below N { 0,1,2,..,N-1 } Q Rational numbers { p/q : p Î Z, q Î N} Â Real numbers C Complex ("Imaginary") numbers { x + iy : x,y Î Â } Intervals [a,b] { r Î Â : a £ r £ b } [a,b) { r Î Â : a £ r < b } (a,b] { r Î Â : a < r £ b } (a,b) { r Î Â : a < r < b } Physical Constants c Speed of light kC Coulomb Constant (4pe0) h Planck Constant 2pEw-1 photonic energy:frequency ratio h Reduced Planck Constant "h bar" (2p)-1h h Reduced Planck Pseudoscalr (2p)-1hi in Â4,1 kB Boltzman constant Molecular energy:temperature ratio Me- Electron mass-energy Qe- Electron charge

 Abbreviation Meaning Example MostSig Most Significant MostSig 8 bits LeastSig Least Significant LeastSig bit _LUT Look Up Table iff If and only-if (Û) whenn When and only-when aka also known as ie. id est (that is) eg. exampli gratia (for example)

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Copyright (c) Ian C G Bell 1998
Web Source: www.iancgbell.clara.net/maths or www.bigfoot.com/~iancgbell/maths
Latest Edit: 18 May 2007.