(linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space. Basis (accounting) Amount paid for an investment, including commissions and other expenses. Basis (topology) A collection of subsets ("basis elements") of a set, such that this collection...
Example Let and be two column vectors defined as follows.These two vectors are linearly independent (see Exercise 1 in the exercise set on linear independence). We are going to prove that and are a basis for the set of all real vectors. Now, take a vector and denote its two entries by...
Fred E. Szabo PhD, in The Linear Algebra Survival Guide, 2015 Dual Space Consider the two-dimensional coordinate space V = ℝ2. A linear functional f is a function ℝ2 → ℝ preserving linear combinations. Each dual space has a basis consisting of linear functionals. It's called a ...
Then, any vector can be written as a linear combination of the basis:where the scalar coefficients are uniquely determined. Remember that the vectoris called the coordinate vector of with respect to the basis . Example Let be a vector space and a basis for . Consider the vectorIts coordinate...
Student[LinearAlgebra] Basis return a basis for a vector space IntersectionBasis return a basis for the intersection of vector space(s) SumBasis return a basis for the direct sum of vector space(s) Calling Sequence Parameters Description Examples Calling
The dimension of a vector space is the number of vectors in any basis for the vector space. Different bases for the same vector space always have the same number of vectors. For example, the vector space M2×2 has the basis {(1000),(0100),(0010),(0001)}....
(especially real property) will be stepped up to current value at the time of the death of the owner, and thus keep down capital gain taxes if the beneficiary of the dead person sells the asset. Example: Daniel Oldboy buys a house for $30,000, and when he dies the place is worth ...
(redirected fromBasis Books) A table or book of tables showing theyieldsofbondsat differentinterest ratesandmaturities. For example, if one is considering the purchase of a bond, one can take thecoupon rateand the maturity and compare them in the basis book to determine the yield. The basis...
Unfortunately, the term orthogonal matrix has become traditional usage in linear algebra. Proof (Abridged) We prove half of part (1) and leave the rest as Exercise 17. Suppose that A is an orthogonal n× n matrix. Then we have AAT = In (why?). Hence, for 1 ≤ i, j≤ n with i...
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