ALGEBRA

Mantrakshar	Hindi	Symbol Name	Meaning / definition	Example
x	X चर	x variable	unknown value to find	when 2x = 4, then x = 2
≡	समानक	equivalence	identical to
≜	परिभाषा के बराबर	equal by definition	equal by definition
:=	परिभाषा के बराबर	equal by definition	equal by definition
~	लगभग समान	approximately equal	weak approximation	11 ~ 10
≈	लगभग समान	approximately equal	approximation	sin(0.01) ≈ 0.01
∝	आनुपातिक	proportional to	proportional to	y ∝ x when y = kx, k constant
∞	अनंत चिन्ह	lemniscate	infinity symbol
≪	से अधिक कम	much less than	much less than	1 ≪ 1000000
≫	से अधिक ज्यादा	much greater than	much greater than	1000000 ≫ 1
( )		parentheses	calculate expression inside first	2 * (3+5) = 16
[ ]		brackets	calculate expression inside first	[(1+2)*(1+5)] = 18
{ }		braces	set
⌊x⌋	फर्श कोष्ठक	floor brackets	rounds number to lower integer	⌊4.3⌋ = 4
⌈x⌉	छत कोष्ठक	ceiling brackets	rounds number to upper integer	⌈4.3⌉ = 5
x!	विस्मयादिबोधक चिह्न	exclamation mark	factorial	4! = 123*4 = 24
delim{]}{x}{]}	लंबवत सलाखों	vertical bars	absolute value	FALSE
f (x)		function of x	maps values of x to f(x)	f (x) = 3x+5
(f ∘ g)		function composition	(f ∘ g) (x) = f (g(x))	f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)
(a,b)	खुला अंतराल	open interval	<m> (a,b) = {x	a < x < b} </m>	x∈ (2,6)
[a,b]	बंद अंतराल	closed interval	<m> [a,b] = {x	a ≤ x ≤ b} </m>	x ∈ [2,6]
∆	बदलाव चिन्ह	delta	change / difference	∆t = t1 - t0
∆		discriminant	Δ = b2 - 4ac
∑		sigma	summation - sum of all values in range of series	∑ xi= x1+x2+…+xn
∑∑		sigma	double summation
∏		capital pi	product - product of all values in range of series	∏ xi=x1∙x2∙…∙xn
e		e constant / Euler's number	e = 2.718281828…	e = lim (1+1/x)x , x→∞
γ		Euler-Mascheroni constant	γ = 0.5772156649…
φ	सुनहरा अनुपात	golden ratio	golden ratio constant
π		pi constant	π = 3.141592654…is the ratio between the circumference and diameter of a circle	c = π⋅d = 2⋅π⋅r

ALGEBRA

Symbol	Symbol Name	Meaning / definition	Example
·	dot	scalar product	a · b
×	cross	vector product	a × b
A⊗B	tensor product	tensor product of A and B	A ⊗ B
\langle x,y \rangle	inner product
[ ]	brackets	matrix of numbers
( )	parentheses	matrix of numbers
A	determinant	determinant of matrix A
det(A)	determinant	determinant of matrix A
<m>delim{vert}{x}{vert}</m>	double vertical bars	norm
AT	transpose	matrix transpose	(AT)ij = (A)ji
A†	Hermitian matrix	matrix conjugate transpose	(A†)ij = (A)ji
A*	Hermitian matrix	matrix conjugate transpose	(A*)ij = (A)ji
A -1	inverse matrix	A A-1 = I
rank(A)	matrix rank	rank of matrix A	rank(A) = 3
dim(U)	dimension	dimension of matrix A	dim(U) = 3

ALGEBRA

LINEAR Algebra symbols