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In mathematics, the absolute value or modulus of a real number, denoted | |, is the non-negative value of without regard to its sign. Namely, | x | = x {\displaystyle |x|=x} if x {\displaystyle x} is a positive number , and | x | = − x {\displaystyle |x|=-x} if x {\displaystyle x} is negative (in which case negating x {\displaystyle x} makes ...
A ⊂ B {\displaystyle A\subset B} may mean that A is a proper subset of B, that is the two sets are different, and every element of A belongs to B; in formula, A ≠ B ∧ ∀ x , x ∈ A ⇒ x ∈ B {\displaystyle A eq B\land \forall {}x,\,x\in A\Rightarrow x\in B} . ⊆. A ⊆ B {\displaystyle A\subseteq B}
Consider a 2-year bond with face value of $100, a 20% semi-annual coupon, and a yield of 4% semi-annually compounded. The total PV will be: V = ∑ i = 1 n P V i = ∑ i = 1 n C F i ( 1 + y / k ) k ⋅ t i = ∑ i = 1 4 10 ( 1 + .04 / 2 ) i + 100 ( 1 + .04 / 2 ) 4 {\displaystyle V=\sum _{i=1}^{n}PV_{i}=\sum _{i=1}^{n}{\frac {CF_{i}}{(1+y/k)^{k ...
In particular, there are 2n + 1 faces in total. The number of them that are k -faces, for k ∈ {−1, 0, ..., n}, is the binomial coefficient . There are specific names for k -faces depending on the value of k and, in some cases, how close k is to the dimensionality n of the polytope.
Eigenface. An eigenface ( / ˈaɪɡən -/ EYE-gən-) is the name given to a set of eigenvectors when used in the computer vision problem of human face recognition. [1] The approach of using eigenfaces for recognition was developed by Sirovich and Kirby and used by Matthew Turk and Alex Pentland in face classification.
The constant satisfies the quadratic equation = + and is an irrational number with a value of φ = 1 + 5 2 = {\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=} 1.618 033 988 749 .... The golden ratio was called the extreme and mean ratio by Euclid , [2] and the divine proportion by Luca Pacioli , [3] and also goes by several other names.
The convex hull of any nonempty subset of the n + 1 points that define an n-simplex is called a face of the simplex. Faces are simplices themselves. In particular, the convex hull of a subset of size m + 1 (of the n + 1 defining points) is an m-simplex, called an m-face of the n-simplex.
a field K and its multiplicative group K×, an abelian totally ordered group (Γ, +, ≥). The ordering and group law on Γ are extended to the set Γ ∪ {∞ } [a] by the rules. ∞ ≥ α for all α ∈ Γ, ∞ + α = α + ∞ = ∞ + ∞ = ∞ for all α ∈ Γ. Then a valuation of K is any map. v : K → Γ ∪ {∞}
Mathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians may express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful or describe mathematics as an art form, (a position taken by G. H. Hardy [1]) or, at a ...
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.