| Symbol | Use | Description | Definition/Example
| º | º | Defined equal | Defined to be equal to
| | º | º | Abreviated notation | Ñx ¦(x) º Ѧ
| | » | » | 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
| | <i> | a<i> | i-vector component |
| | Ù | aÙb | Outer product | (akÙbm = (ab)<m+k>
| | ¿ | a¿b | Contractive inner product | ak¿bm = (ab)<m-k>
| | . | 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)<Max>
| | ¨ | 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<i>
| | § | a§ | Reverse | åi(-1)½ i(i-1)a<i>
| | © | 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
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