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For a change of basis, the formula of the preceding section applies, with the same change-of-basis matrix on both sides of the formula. That is, if M is the square matrix of an endomorphism of V over an "old" basis, and P is a change-of-basis matrix, then the matrix of the endomorphism on the "new" basis is .
A projective basis is + points in general position, in a projective space of dimension n. A convex basis of a polytope is the set of the vertices of its convex hull. A cone basis [5] consists of one point by edge of a polygonal cone. See also a Hilbert basis (linear programming).
In the definition of similarity, if the matrix P can be chosen to be a permutation matrix then A and B are permutation-similar; if P can be chosen to be a unitary matrix then A and B are unitarily equivalent. The spectral theorem says that every normal matrix is unitarily equivalent to some diagonal matrix.
The distinction between extraordinary assumptions and hypothetical conditions can be a matter of law or professional standards in the field of real estate appraisal in the United States where the distinction is not only codified in USPAP, but enforced by various state real estate appraiser commissions or professional boards. However, the ...
When it comes to selling a home there's a lot to know beyond staging and setting a reasonable list price. As with any industry, there are real estate definitions (homestead, quit-claim) and a set ...
The sales comparison approach (SCA) is a real estate appraisal valuation method that relies on the assumption that a matrix of attributes or significant features of a property drive its value. For examples, in the case of a single family residence, such attributes might be floor area, views, location, number of bathrooms, lot size, age of the ...
A broker price opinion (BPO) is a real estate professional’s dollar estimate of a property’s worth. It is an opinion, but one often backed up by the selling prices of comparable homes in ...
The matrix Q is the change of basis matrix of the similarity transformation. Essentially, the matrices A and Λ represent the same linear transformation expressed in two different bases. The eigenvectors are used as the basis when representing the linear transformation as Λ.