# 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
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Amounts received in excess of the tax basis up to the amount of the cash surrender value are taxed at ordinary income rates, and
As the transfer tax system continues to ebb in importance, Congress should institute a permanent carryover tax basis regime.
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 result of this new reporting requirement is that beneficiaries must now use the value of assets reported on the Form 706 Estate Tax Return as their income tax basis.
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.
When an individual sells or otherwise transfers securities (i.e., stocks, bonds, mutual fund shares, etc.) from holdings that were purchased or acquired on different dates or at different prices (or tax bases), he must generally be able to identify the lot from which the transferred securities originated in order to determine his tax basis and holding period.
An allocation of the tax basis of goodwill would be included.
* Deductible casualty losses; payments received for granting an easement: and residential energy and first-time homebuyer credits may result in taxpayers' reducing the tax basis in their homes.
Proponents of this technique argue that, as long as the spouse was granted the general power of appointment at least a year before the spouse's death, the income tax basis should be adjusted to fair market value at the date of the spouse's death.
Since it is mathematically possible for cumulative cost of insurance charges to exceed cumulative premiums, can a policy have a negative tax basis?
Generally, in the case of a partnership's distribution to a partner, gain is not recognized except to the extent that any money distributed exceeds the adjusted tax basis of the partner's interest in the partnership immediately before the distribution (Sec.

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