# 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 ?
Depending on its exit strategy, a buyer should be aware of these adverse effects on the tax basis of the shares purchased.
29 per STWD share would be a non-taxable return of capital and would reduce the tax basis of each of your STWD shares.
Thus, it is more important than ever for taxpayers to accurately track the tax basis in their homes.
Also, the grantor may find it necessary to know tax basis when gifting property to a charitable organization.
2) Determined by multiplying \$10,000 by the applicable tax basis allocation percentage in the table above.
Tracing method: If the tracing method is applied, the entire tax basis of the CD partnership interest should be allocated to A when AB distributes the CD partnership interest to A and B, to preserve B's contribution of Sec.
In 1981, recognizing the extensive undertaking of retrieving tax basis information from thousands of shareholders, the IRS issued a revenue procedure affording taxpayers an alternative to surveying each of the target shareholders.
Under current law, the ability to obtain an increased deduction over tax basis for the donation of off-spec food can be challenging because the food must meet the same tax requirements as other food; that is, it must constitute inventory for tax purposes and have a supportable FMV above tax basis.
According to several authorities, a taxpayer does not have any tax basis in qualified retirement plan assets such as IRAs or 401(k)s because the Employee Retirement Income Security Act of 1974 established a taxpayer has zero basis in a traditional IRA because no taxes were paid on either the contributions or earnings.
338 election to receive a step up in the selling corporation's assets' tax basis, but the buyer would then have to pay a corporate-level income tax.
The suspended gain is the amount by which the fair market value of the shares exceeds their tax basis and the amount of surplus that is eligible for a section 93 election.
Gain or loss is measured by how much the fair market value of the property exceeds or falls short of its tax basis, which is customarily determined by original cost less depreciation.

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