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Basis
Basis may refer to: Finance and accounting *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 **Basis (options), the value differential between a call option and a put option **Basis swap, an interest rate swap *Cost basis, in income tax law, the original cost of property adjusted for factors such as depreciation *Tax basis, cost of an asset and technology *Basis function *Basis (linear algebra) **Dual basis **Orthonormal basis **Schauder basis *Basis (universal algebra) *Basis of a matroid *Generating set of an ideal: **Gröbner basis ** Hilbert's basis theorem *Generating set of a group *Base (topology) *Change of basis *Greedoid *Normal basis *Polynomial basis *Radial basis function *Sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Set (chemistry)
In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer. The use of basis sets is equivalent to the use of an approximate resolution of the identity: the orbitals , \psi_i\rangle are expanded within the basis set as a linear combination of the basis functions , \psi_i\rangle \approx \sum_\mu c_ , \mu\rangle, where the expansion coefficients c_ are given by c_ = \sum_\nu \langle \mu, \nu \rangle^ \langle \nu , \psi_i \rangle. The basis set can either be composed of atomic orbitals (yielding the linear combination of atomic orbitals approach), which is the usual choice within the quantum chemistry community; plane waves which are typically used within the solid state community, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis (linear Algebra)
In mathematics, a set of vectors in a vector space is called a basis if every element of may be written in a unique way as a finite linear combination of elements of . The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to . The elements of a basis are called . Equivalently, a set is a basis if its elements are linearly independent and every element of is a linear combination of elements of . In other words, a basis is a linearly independent spanning set. A vector space can have several bases; however all the bases have the same number of elements, called the ''dimension'' of the vector space. This article deals mainly with finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces. Definition A basis of a vector space over a field (such as the real numbers or the complex numbers ) is a linearly independent subset of that spans . This me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radial Basis Function
A radial basis function (RBF) is a real-valued function \varphi whose value depends only on the distance between the input and some fixed point, either the origin, so that \varphi(\mathbf) = \hat\varphi(\left\, \mathbf\right\, ), or some other fixed point \mathbf, called a ''center'', so that \varphi(\mathbf) = \hat\varphi(\left\, \mathbf-\mathbf\right\, ). Any function \varphi that satisfies the property \varphi(\mathbf) = \hat\varphi(\left\, \mathbf\right\, ) is a radial function. The distance is usually Euclidean distance, although other metrics are sometimes used. They are often used as a collection \_k which forms a basis for some function space of interest, hence the name. Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network; this was the context in which they were originally applied to machine learning, in work by David Broomhead and David Lowe in 1988, which st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Trading
Basis trading is a financial trading strategy which consists of the purchase of a particular financial instrument or commodity and the sale of its related derivative (for example the purchase of a particular bond and the sale of a related futures contract). Basis trading is done when the investor feels that the two instruments are mispriced relative to one other and that the mispricing will correct itself so that the gain on one side of the trade will more than cancel out the loss on the other side of the trade. In the case of such a trade taking place on a security and its related futures contract, the trade will be profitable if the purchase price plus the net cost of carry is less than the futures price. Basis of futures Basis can be defined as the difference between the spot price of a given cash market asset and the price of its related futures contract.Hull, "Options, Futures and Other Derivatives", 6 Ed, Prentice Hall There will be a different basis for each delivery mont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Of Futures
Basis trading is a financial trading strategy which consists of the purchase of a particular financial instrument or commodity and the sale of its related derivative (for example the purchase of a particular bond and the sale of a related futures contract). Basis trading is done when the investor feels that the two instruments are mispriced relative to one other and that the mispricing will correct itself so that the gain on one side of the trade will more than cancel out the loss on the other side of the trade. In the case of such a trade taking place on a security and its related futures contract, the trade will be profitable if the purchase price plus the net cost of carry is less than the futures price. Basis of futures Basis can be defined as the difference between the spot price of a given cash market asset and the price of its related futures contract.Hull, "Options, Futures and Other Derivatives", 6 Ed, Prentice Hall There will be a different basis for each delivery month ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis (options)
Basis trading is a financial trading strategy which consists of the purchase of a particular financial instrument or commodity and the sale of its related derivative (for example the purchase of a particular bond and the sale of a related futures contract). Basis trading is done when the investor feels that the two instruments are mispriced relative to one other and that the mispricing will correct itself so that the gain on one side of the trade will more than cancel out the loss on the other side of the trade. In the case of such a trade taking place on a security and its related futures contract, the trade will be profitable if the purchase price plus the net cost of carry is less than the futures price. Basis of futures Basis can be defined as the difference between the spot price of a given cash market asset and the price of its related futures contract.Hull, "Options, Futures and Other Derivatives", 6 Ed, Prentice Hall There will be a different basis for each delivery mont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cost Basis
Basis (or cost basis), as used in United States tax law, is the original cost of property, adjusted for factors such as depreciation. When property is sold, the taxpayer pays/(saves) taxes on a capital gain/(loss) that equals the amount realized on the sale minus the sold property's basis. Cost basis is needed because tax is due based on the gain in value of an asset. For example, if a person buys a rock for $20, and sells the same rock for $20, there is no tax, since there is no profit. If, however, that person buys a rock for $20 and then sells the same rock for $25, then there is a capital gain on the rock of $5, which is thus taxable. The purchase price of $20 is analogous to cost of sales. Typically, capital gains tax is due only when an asset is sold. However the rules for this are very complicated. If tax is paid because the value has increased, the new value will be the cost basis for any future tax. Internal Revenue Service (IRS) Publication 551 contains the IRS's defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjusted Basis
In tax accounting, adjusted basis is the net cost of an asset after adjusting for various tax-related items. Adjusted Basis or Adjusted Tax Basis refers to the original cost or other basis of property, reduced by depreciation deductions and increased by capital expenditures. Example: Brad buys a lot for $100,000. He then erects a retail facility for $600,000, then depreciates the improvements for tax purposes at the rate of $15,000 per year. After three years his adjusted tax basis is $655,000 100,000 + $600,000 - (3 x $15,000) Adjusted basis is one of two variables in the formula used to compute gains and losses when determining gross income for tax purposes. The Amount Realized – Adjusted Basis tells the amount of Realized Gain (if positive) or Realized Loss (if negative). Statutory definition Section 1012 of the Internal Revenue Code defines “basis” as a taxpayer’s cost in acquiring property, except as provided in Sections 1001-1092. Section 1016 then lists 27 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gröbner Basis
In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring over a field . A Gröbner basis allows many important properties of the ideal and the associated algebraic variety to be deduced easily, such as the dimension and the number of zeros when it is finite. Gröbner basis computation is one of the main practical tools for solving systems of polynomial equations and computing the images of algebraic varieties under projections or rational maps. Gröbner basis computation can be seen as a multivariate, non-linear generalization of both Euclid's algorithm for computing polynomial greatest common divisors, and Gaussian elimination for linear systems. Gröbner bases were introduced in 1965, together with an algorithm to compute them (Buchberger's algorithm), by Bruno Buchberger in his Ph.D. thesis. He named them after h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Swap
A basis swap is an interest rate swap which involves the exchange of two floating rate financial instruments. A basis swap functions as a floating-floating interest rate swap under which the floating rate payments are referenced to different bases. The existence of a basis arises from demand and supply imbalances and where, for example, a basis is due for a borrower seeking dollars, this is indicative of a synthetic dollar interest rate in the FX market pricing higher than the direct dollar interest rate. The existence of the basis is a violation of the covered interest rate parity (CIP) condition. Usage of basis swaps for hedging Basis risk occurs for positions that have at least one paying and one receiving stream of cash flows that are driven by different factors and the correlation between those factors is less than one. Entering into a Basis Swap may offset the effect of gains or losses resulting from changes in the basis, thus reducing basis risk. # against exposure to curre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthonormal Basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space ''V'' with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space \R^n is an orthonormal basis, where the relevant inner product is the dot product of vectors. The image of the standard basis under a rotation or reflection (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for \R^n arises in this fashion. For a general inner product space V, an orthonormal basis can be used to define normalized orthogonal coordinates on V. Under these coordinates, the inner product becomes a dot product of vectors. Thus the presence of an orthonormal basis reduces the study of a finite-dimensional inner product space to the study of \R^n under dot product. Every finite-dimensional inner product space has an orthonormal basis, which may be ob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Basis
In linear algebra, given a vector space ''V'' with a basis ''B'' of vectors indexed by an index set ''I'' (the cardinality of ''I'' is the dimension of ''V''), the dual set of ''B'' is a set ''B''∗ of vectors in the dual space ''V''∗ with the same index set ''I'' such that ''B'' and ''B''∗ form a biorthogonal system. The dual set is always linearly independent but does not necessarily span ''V''∗. If it does span ''V''∗, then ''B''∗ is called the dual basis or reciprocal basis for the basis ''B''. Denoting the indexed vector sets as B = \_ and B^ = \_, being biorthogonal means that the elements pair to have an inner product equal to 1 if the indexes are equal, and equal to 0 otherwise. Symbolically, evaluating a dual vector in ''V''∗ on a vector in the original space ''V'': : v^i\cdot v_j = \delta^i_j = \begin 1 & \text i = j\\ 0 & \text i \ne j\text \end where \delta^i_j is the Kronecker delta symbol. Introduction To perform operations with a vector, we must ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
