====== 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! = 1*2*3*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	|

[[:en:algebra | ALGEBRA ]] 





==== LINEAR Algebra symbols ====

^ hindi		^	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	|