A Primer on Index Notation
Vector Notation Index Notation ~a~b = C a ib j = C ij The term “tensor product” refers to the fact that the result is a ten-sor (e) Tensor product of two tensors: Vector Notation Index Notation A·B = C A ijB jk = C ik The single dot refers to the fact that only the inner index is to be summed Note that this is not an inner product
Notation: Operators
#+b " 2 #) = aA " 1 #+bA" 2 # •a and b are arbitrary c-numbers Notation: –Generally, we will follow Cohen-Tannoudji, and use capital letters for operators and lower-case letters for c-numbers –Another common convention is to distinguish operators by giving them a ‘^’ •I may use this occasionally aˆAˆˆ
Sets and Probability - Texas A&M University
be written as {a,b,c,d,e, f,g,h,i, j} in roster notation If we wanted to refer to this set without writing all the elements, we could define the set in terms of its
Vectors & Matrices : suffix notation
its value if we want to work out a specific component For example: a = (b · c)d Here, each component of d is scaled by the same factor to get a, so a1 = (b · c)d1, etc In suffix notation, we write a i = b jc jd i The suffix i is “free”, and we are free to set i = 1,2,3 to work out specific components But b jc
Index Notation for Vector Calculus
index for~b is completely independent of that used for~a We will first write out the scalar product ~a ·~b in long-hand form, and then express it more compactly using some of the properties of index notation ~a·~b = X3 i=1 a ieˆ i · X3 j=1 b jˆe j = X3 i=1 X3 j=1 [(a iˆe i)·(b jˆe j)] = X3 i=1 X3 j=1 [a ib j (ˆe i · ˆe j
divisibility - sitesmillersvilleedu
1-17-2019 Divisibility If aand bare integers, adivides bif there is an integer csuch that ac= b The notation a bmeans that adivides b For example, 3 6, since 3·2 = 6
Logic, Sets, and Proofs
David A Cox and Catherine C McGeoch Amherst College 1 Logic Logical Statements A logical statement is a mathematical statement that is either true or false Here we denote logical statements with capital letters A;B Logical statements be combined to form new logical statements as follows: Name Notation Conjunction A and B Disjunction A or B
Name Orbital Notation - Mrs Schlitts Chemistry Website
B) C) D) 4 Which orbital notation correctly represents a noble gas in the ground state? A)6 B)2 C)8 D)4 5 What is the total number of unpaired electrons in an
Set Operations - homepagesmathuicedu
A⊆B if every element of A is also an element of B If A and B are both subsets of each other, then we say the sets are equal If A is a subset of B and there is at least 1 element of B that is not in A, then we say A is a proper subset of B, denoted A⊂B The universal set U is the set containing all elements for the problem we are discussing
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