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 Basisthat 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 Basiscan 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 classic literature ?
The majority will never be withdrawn from the obscurity of the manuscripts on which the patient care of their authors inscribed them; others have been printed in full and serve as the main basis for our knowledge of the events of the period.
The SOCIAL CONTRACT founded upon this basis will be a perpetual pact between those who have and those who have not.
But like the snout of the boar shall my word grub up the basis of your souls; a ploughshare will I be called by you.
That your virtue is your Self, and not an outward thing, a skin, or a cloak: that is the truth from the basis of your souls, ye virtuous ones
It is among these frustrated impulses that I would find the biological basis of the unfulfilled wish.
Most important of all--he must get back without delay: he would have to make haste to put his new project to the peasants before the sowing of the winter wheat, so that the sowing might be undertaken on a new basis.
The school is operated by BASIS Global, LLC, with management assistance from BASIS.
A slew of court cases and rulings were issued on an S shareholder's adjusted basis for loss purposes.
The initial tax basis includes the cost of the home plus all settlement and closing costs.
If your company engaged in a tax-free stock acquisition and has already computed the tax basis of the acquired stock or believe that in the future you may need to do so, you should read on.
As a result of the $25 reduction in the mortgage, you may reduce your basis in the property by $25 without recognizing DOI Income.
The base rate we use is the manager's full fee, but in order to earn that full fee the manager must perform a fee-adjusted 200 basis points over the benchmark.