Let n be a positive integer, and let V be a 2n-dimensional vector space over an algebraically
closed field K of characteristic 0.
and colleagues present the results of their research investigating the ability of elementary school students to reason algebraically
and to learn algebra.
Another approach is to assign algebraically
independent values to the nonzeros (i.
W] is again a polynomial algebra, and it can be generated by n algebraically
independent homogeneous polynomials [f.
The approach computes the local Denef- Loeser motivic zeta function of a quasi-ordinary power series of arbitrary dimension over an algebraically
closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities.
UNDERWOOD, A block Lanczos algorithm for computing the q algebraically
largest eigenvalues and a corresponding eigenspace of large, sparse, real symmetric matrices, Proc.
He shows how these and others can be described and represented in Hilbert space, formulates the reasoning within each algebraically
, and explains that they depend essentially on the geometry of the information space.
Topics include non-Euclidean geometry in the fourth dimension, space and hyperspace, the fourth dimension algebraically
considered, the ascending state of dimensions, possible measurements and forms in a system of four dimensions, and several articles speculating on what happens beyond length, breadth and depth.
, the relationship between the ratios can be expressed:
His principal goal is to examine the known results on the equivalence theory and related matters such as the Witt and Witt-Grothendieck groups, over the classical fields: algebraically
closed, real closed, finite, local and global.
The change of basis may be accomplished algebraically
by use of the matrix G given by [G.
This formulation, with a one-period lag on the vector of levels, is algebraically
equivalent to Johansen's equation, where the levels are lagged k periods.