# basis

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## basis

Maths (of a vector space) a maximal set of linearly independent vectors, in terms of which all the elements of the space are uniquely expressible, and the number of which is the dimension of the space

## Basis

in mathematics, a set of linearly independent vectors taken in a certain order and plotted from a common origin. For vectors in three-dimensional space, any set of three vectors that are not parallel to the same plane can be used as a basis. If the vectors making up the basis are mutually orthogonal, then the basis is said to be orthogonal; if the vectors are of unit length, then the basis is an orthonormal basis. In the general case of an n-dimensional vector space, any set of n linearly independent vectors can be taken as a basis.

## basis

[′bā·səs]
(mathematics)
A set of linearly independent vectors in a vector space such that each vector in the space is a linear combination of vectors from the set.
References in periodicals archive ?
Further, aside from the foregoing technological, political, and economic changes, the relaxation of the estate, gift, and generation-skipping taxes (collectively, transfer taxes) that began in 1976 and continues today (25) makes the institution of a carryover tax basis regime imperative.
Essentially, the seller in a life settlement transaction would have the same tax basis as someone who surrendered a policy.
While a purchaser is generally incentivized to engage in an asset acquisition in order to avoid acquiring unwanted liabilities of a target, as well as to obtain a tax basis step-up, (4) a seller is typically incentivized to engage in a stock sale.
The death of a partner in a general, an LP or LLC can have additional tax basis complications that are often overlooked by tax practitioners.
Similarly, if the shareholder's tax basis in the shares redeemed is minimal or zero, the sale or exchange treatment of the transaction may not have a material effect on taxable income.
Father's tax basis is \$90,000, and the properly has a FMV of \$30,000.
To promote home ownership and in recognition of the difficulties of ascertaining a home's tax basis, Congress has traditionally offered homeowners numerous tax benefits.
Assume the only contributions to the trust are separate assets of James worth \$500,000, with an income tax basis of \$100,000.
For property acquired by gift, grantees use the same tax basis as the grantor's tax basis.
Per share tax basis in McDermott shares owned before the B&W spin off:
732 and allocate the tax basis of the distributed resulting partnership interest strictly in accordance with the pro rata percentage the partner is receiving (the pro rata method).
For lifetime gifts, under IRC section 1015, a carryover tax basis rule applies.

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