# Algebra Symbols

Algebra is a part of mathematics which deals with symbols and the rules for manipulating those symbols. In algebra, those symbols represent quantities without fixed values, called as variables. Just how sentences describe relationships between specific words, in algebra, equations describe relationships between variables.

Math can be difficult for allot of people out there. However, it is crucial to recognize that even symbols, used in algebra, have names, and those names are made up of letters and words.

 Symbol Symbol Name Meaning / definitio Example ≡ equivalence identical to x x variable unknown value to find when 2x = 4, then x = 2 := equal by definition equal by definition ≜ equal by definition equal by definition ≈ approximately equal approximation sin(0.01) ≈ 0.01 ~ approximately equal weak approximation 11 ~ 10 ∞ lemniscate infinity symbol ∝ proportional to proportional to y ∝ x when y = kx, k constant ≫ much greater than much greater than 1000000 ≫ 1 ≪ much less than much less than 1 ≪ 1000000 [ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18 ( ) parentheses calculate expression inside first 2 * (3+5) = 16 ⌊x⌋ floor brackets rounds number to lower integer ⌊4.3⌋= 4 { } braces set x! exclamation mark factorial 4! = 1*2*3*4 = 24 ⌈x⌉ ceiling brackets rounds number to upper integer ⌈4.3⌉= 5 f (x) function of x maps values of x to f(x) f (x) = 3x+5 | x | single vertical bar absolute value | -5 | = 5 (a,b) open interval (a,b) = {x | a < x < b} x ∈ (2,6) (f ∘g) function composition (f ∘g) (x) = f (g(x)) f (x)=3x, g(x)=x-1 ⇒(f ∘g)(x)=3(x-1) ∆ delta change / difference ∆t = t1 – t0 [a,b] closed interval [a,b] = {x | a ≤ x ≤ b} x ∈ [2,6] ∑ sigma summation – sum of all values in range of series ∑ xi= x1+x2+…+xn ∆ discriminant Δ = b2 – 4ac ∑∑ sigma double summation $\sum_{j=1}^{2} \sum_{i=1}^{8} xi,j = \sum_{i=1}^{8}xi,j + \sum_{i=1}^{8} xi,2$ e e constant / Euler’s number e = 2.718281828… e = lim (1+1/x)x , x→∞ ∏ capital pi product – product of all values in range of series ∏ xi=x1∙x2∙…∙xn γ Euler-Mascheroni  constant γ = 0.527721566… π pi constant π = 3.141592654… is the ratio between the circumference and diameter of a circle c = π·d = 2·π·r φ golden ratio golden ratio constant

### Linear Algebra Symbols

 Symbol Symbol Name Meaning / definition Example × cross vector product a × b ∙ dot scalar product a ∙ b $\left \langle x,y \right \rangle$ inner product A⊗B tensor product tensor product of A and B A ⊗ B [ ] brackets matrix of numbers ( ) parentheses matrix of numbers det(A) determinant determinant of matrix A | A | determinant determinant of matrix A A T transpose matrix transpose (AT)ij = (A)ji || x || double vertical bars norm A † Hermitian matrix matrix conjugate transpose (A†)ij = (A)ji A -1 inverse matrix A A-1 = I dim(U) dimension dimension of matrix A rank(U) = 3 rank(A) matrix rank rank of matrix A rank(A) = 3