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The elements of a basis are called basis vectors. Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B. [1] In other words, a basis is a linearly independent spanning set.
Adjusted basis, the net cost of an asset after adjusting for various tax-related items; Basis point, 0.01%, often used in the context of interest rates; Basis trading, a trading strategy consisting of the purchase of a security and the sale of a similar security Basis of futures, the value differential between a future and the spot price
Every vector a in three dimensions is a linear combination of the standard basis vectors i, j and k.. In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors, each of whose components are all zero, except one that equals 1. [1]
In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors .
The modified cash basis of accounting, combines elements of both accrual and cash basis accounting. Some forms of the modified cash basis record income when it is earned but deductions when expenses are paid out. In other words, the recording of income is on an accrual basis, while the recording of expenses is on the cash basis.
A fundamental cycle basis may be formed from any spanning tree or spanning forest of the given graph, by selecting the cycles formed by the combination of a path in the tree and a single edge outside the tree. Alternatively, if the edges of the graph have positive weights, the minimum weight cycle basis may be constructed in polynomial time.
The classical normal basis theorem states that there is an element such that {():} forms a basis of K, considered as a vector space over F. That is, any element α ∈ K {\displaystyle \alpha \in K} can be written uniquely as α = ∑ g ∈ G a g g ( β ) {\textstyle \alpha =\sum _{g\in G}a_{g}\,g(\beta )} for some elements a g ∈ F ...
A Gröbner basis is minimal if all leading monomials of its elements are irreducible by the other elements of the basis. Given a Gröbner basis of an ideal I, one gets a minimal Gröbner basis of I by removing the polynomials whose leading monomials are multiple of the leading monomial of another element of the Gröbner basis. However, if two ...