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Topic: Flag (linear algebra)

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	PlanetMath: flag
		More generally, a flag can be defined as a maximal chain in a partially ordered set.
		This is version 6 of flag, born on 2002-06-01, modified 2006-09-23.
		Object id is 2994, canonical name is Flag.
	planetmath.org /encyclopedia/Flag.html (150 words)

	Cornell Math - Thesis Abstracts (Combinatorics)
		The flag Whitney numbers of a geometric lattice count the number of chains of the lattice with elements having specified ranks.
		We prove the existence of a subalgebra of Solomon's descent algebra in which elements are sums of permutations that share a common peak set.
		Given d+1 linear forms on a d-dimensional projective variety, the Chow form is a polynomial in the coefficients of the linear forms (unique up to multiplication by a nonzero constant) which is zero if and only if the linear forms have a common zero on the variety.
	www.math.cornell.edu /Research/Abstracts/combinatorics.html (1886 words)

	Cornell Math - Thesis Abstracts (Algebra)
		With these examples as motivation, we abstract the notion of a shuffle algebra which captures the connection between the algebraic structure of the shuffles and the geometry of the Coxeter groups.
		Delta categories are defined; these are algebraic objects that generalize groups or bialgebras, in the sense that attached to them there is a monoidal category of representations.
		This thesis studies linear and non-linear conditions on the flag f-vectors of several classes of polytopes.
	www.math.cornell.edu /~www/Research/Abstracts/algebra.html (5306 words)

	Holistic Algebra
		Students often complain that they cannot see the point of learning algebra so all of the teaching of skills here is placed within contexts.
		It is not suggested that this unit should replace the skills practice traditionally used in the teaching of algebra.
		As maths teachers we often refer to a letter symbol as a variable, when sometimes we mean an unknown specific value, sometimes a generalised unknown, and sometimes we really do mean a variable.
	www.nzmaths.co.nz /algebra/Units/Holisticalgebra.aspx (2980 words)

	Flag (linear algebra) - Wikipedia, the free encyclopedia
		In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a vector space V.
		A partial flag can be obtained from a complete flag by deleting some of the subspaces.
		In an infinite-dimensional space V, as used in functional analysis, the flag idea generalises to a subspace nest, namely a collection of subspaces of V that is a total order for inclusion and which further is closed under arbitrary intersections and closed linear spans.
	en.wikipedia.org /wiki/Flag_(linear_algebra) (264 words)

	ACM Sigplan Notices 27, 8 (Aug. 1992), 89-98.
		Linear logic conserves accessibility, and hence provides a mechanical metaphor which is more appropriate for a distributed-memory parallel processor in which copying is explicit.
		Linear Lisp can be used in a "shared-heap-memory" multiprocessing configuration, in which the memory to be shared is actually the hash consed heap.
		Linear Lisp is an ideal environment for symbolic algebra, since it provides the efficiencies of sharing, including fast copying and fast equality checking [Goto76], without the problems.
	home.pipeline.com /~hbaker1/LinearLisp.html (4324 words)

	CS267: Supplementary Notes on Floating Point
		This lecture is a quick survey of issues in floating point arithmetic relevant to numerical linear algebra, including parallel numerical linear algebra.
		This means that the floating point result fl(a op b) of the exact operation (a op b) is the nearest floating point number to (a op b), breaking ties by rounding to the floating point number whose bottom bit is zero (the "even" one).
		This approach is ubiquitous in numerical linear algebra, where x and f(x) are usually vectors and/or matrices, and we use norms to bound the error:
	www.cs.berkeley.edu /~demmel/cs267/lecture21/lecture21.html (4277 words)

	Braingle: 'Am I a Signal?' Riddle
		In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a vector space V. The most common definition of flag is the emblem that usually consists of a rectangular piece of cloth of distinctive design.
		On the cigar, the flag is an extension of the wrapper shaped to finish the head of the cigar.
		Sometimes it is tied off in a pigtail, and the flag is used instead of a cap.
	www.braingle.com /33502.html (255 words)

	Catalogue of GP/PARI Functions: Vectors, matrices, linear algebra and sets (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-25)
		flag then indicates a precision, which should be between 0.5 and 1.0 times the number of decimal digits to which x was computed.
		If flag = 0, the method used is essentially the same as for computing the adjoint matrix, i.e.computing the traces of the powers of A. If flag = 1, uses Lagrange interpolation which is almost always slower.
		If this flag is set, X is allowed to be of the form D or [U,V,D] as would normally be output with the cleanup flag unset.
	www.skalatan.de.cob-web.org:8888 /pariguide/doc/Vectors,_matrices,_linear_algebra_and_sets.html (4049 words)

	Research in Algebra \| Ring Theory (Site not responding. Last check: 2007-10-25)
		Later, it was realised that commutative noetherian rings are one of the building blocks of modern algebraic geometry, leading to their study both abstractly and in examples.
		Typically, the representation theory of such algebras is closely related to the geometry of the prime spectrum of centre of the algebra.
		These algebras are very new (they were introduced by Etingof and Ginzburg in 2000), so the foundations for their study are still being laid.
	www.maths.gla.ac.uk /research/groups/algebra/rings.htm (988 words)

	UNT Department of Mathematics: Algebra Seminar
		Then as a specific example we'll revisit the representations of the Lie algebra of 2 by 2 matrices that Charlie constructed using generators and relations and show how they arise naturally when you study the geometry divisors) or topology (line bundles) of the projective plane.
		Abstract: The extremal projector of a reductive Lie algebra is an operator in a certain extension of its universal enveloping algebra which projects any finite dimensional representation to its highest weight vectors.
		In this talk we are going to show, that for the special case of principal blocks of general linear groups with abelian Sylow-l-subgroups this is true, by an explicit verification relating the complex X to the Coxeter complex of the corresponding Weyl group.
	www.math.unt.edu /seminars/algebra.shtml (2410 words)

	Catalogue of GP/PARI Functions: Vectors, matrices, linear algebra and sets (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-25)
		Otherwise, the value of flag determines the algorithm used; in the current version of PARI, we suggest to use non-negative values, since it is by far the fastest and most robust implementation.
		If flag = 3, uses Batut's algorithm, but outputs [H,U,P], such that H and U are as before and P is a permutation of the rows such that P applied to xU gives H. The matrix U is smaller than with flag = 1, but may still be large.
		The result is a three-component vector, the first component being the number of vectors found, the second being the maximum norm found, and the last vector is a matrix whose columns are the vectors found, only one being given for each pair ± v (at most m such pairs).
	pari.math.u-bordeaux1.fr.cob-web.org:8888 /dochtml/html.stable/Vectors,_matrices,_linear_algebra_and_sets.html (4693 words)

	LINEAR
		An operator can be declared linear in its first argument over powers of its second argument by the declaration linear.
		The operator being declared must have at least two arguments, and the second one must be a kernel.
		Programming in symbolic as well as algebraic mode allows you a wider range of techniques than just algebraic mode alone.
	www.reduce-algebra.com /docs/help/r38_0200.html (6345 words)

	Maths - Cilfford / Geometric Algebra - Martin Baker
		There are a number of different ways to think about this algebra, different people might react differently to the ways to describe Geometric Algebra (GA), an approach that may not help one person may just help the whole thing 'click' with another person.
		Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (Fundamental Theories of Physics).
		It covers the algebra and calculus of multivectors of any dimension and does not have any specific material on 3D multivectors.
	www.euclideanspace.com /maths/algebra/clifford/concepts (391 words)

	Julianna Tymoczko
		My research is primarily in combinatorial and topological aspects of linear algebraic groups.
		In my thesis I studied Hessenberg varieties, which are subvarieties of the full flag variety parametrized by a Lie algebra element and a certain subspace of the Lie algebra.
		Special examples of Hessenberg varieties include the Springer fiber (a variety closely tied to representation theory), the Peterson variety (related to the quantum cohomology of the flag variety), the space of Hessenberg matrices for a linear operator M (important in numerical analysis), and the entire flag variety itself.
	www.math.lsa.umich.edu /~tymoczko (576 words)

	Maxima Manual - Matrices and Linear Algebra (Site not responding. Last check: 2007-10-25)
		The flags that affect this function are: NONDIAGONALIZABLE[FALSE] will be set to TRUE or FALSE depending on whether the matrix is nondiagonalizable or diagonalizable after an EIGENVECTORS command is executed.
		In this way, a rich variety of algebraic structures may be simulated.
		The flags mentioned in the description of the EIGENVECTORS command have the same effects in this one as well.
	www.ma.utexas.edu /maxima/maxima_25.html (3133 words)

	flag - OneLook Dictionary Search
		Flag (Yellow) : A Modern Herbal, 1931, by Mrs.
		Phrases that include flag: flag day, fl flag, blue flag, sweet flag, flag waving, more...
		Words similar to flag: droop, iris, banner, ensign, flagged, flagging, flagstone, fleur-de-lis, pin, sag, swag, tire, ease off, ease up, languish, national flag, signal flag, slacken off, slack off, sword lily, more...
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=flag (632 words)

	NUS Dept of Maths Algebra and Number Theory Seminars
		Let G be the general linear group or the symplectic group over the complex number field, and U be its maximal unipotent subgroup.
		We describe the flag algebra in terms of Gelfand-Tsetlin patterns.
		In particular, we show that the flag algebra is a flat deformation of a toric variety.
	www.math.nus.edu.sg /~mattankm/AlgSem (757 words)

	Math 55a: Honors Advanced Calculus and Linear Algebra (Fall 2002)
		A flag in a finite dimensional vector space V is a sequence of subspaces {0}=V
		The dimension of the space of generalized c-eigenvalues (i.e., of the nilspace of T-cI) is usually called the algebraic multiplicity of c (since it's the multiplicity of c as a root of the characteristic polynomial of T), to distinguish it from the ``geometric multiplicity'' which is the dimension of ker(T-cI).
		The ``top exterior power'' is a subspace of the ``exterior algebra'' of V, which is the quotient of the tensor algebra by the ideal generated by {v*v: v in V}.
	www.math.harvard.edu /~elkies/M55a.05/index.html (2742 words)

	SFSU Algebra-Geometry-Combinatorics Seminar (Spring 2006)
		Abstract: Given d distinct points on a line, elementary linear algebra shows that one can find a polynomial function of degree d-1 taking specified values at each of the points--this is called interpolation.
		Abstract: Integer linear optimization, that is the problem of optimizing a linear functional over the integer points of a polyhedron, is NP-hard.
		They are intimately related to the classical finite dimensional semisimple Lie algebras and to their infinite dimensional counterparts - the affine and indefinite Kac-Moody algebras.
	math.sfsu.edu /beck/seminar/seminar.s06.html (2005 words)

	Algebra-Number Theory Seminar Abstracts
		Then I'll talk of our new approach to Faltings' "almost purity" (which is at the heart of his version of p-adic Hodge theory).
		There are important connections to the study of nearby cycles and perverse sheaves on affine flag varieties, which I will highlight.
		We also discuss possible generalizations to the case of schemes over rings of algebraic integers.
	www.math.umd.edu /research/seminars/algebra/abstracts01-02.html (1148 words)

	Thomas J. Haines - homepage
		Formulae relating the Bernstein and Iwahori-Matsumoto presentations of an affine Hecke algebra, (with A. Pettet), J. Algebra, vol.
		Iwahori-Hecke Algebras, pdf (with R. Kottwitz and A. Prasad).
		A fairly self-contained treatment of basic facts about the Iwahori-Hecke algebra of a split p-adic group, including Bernstein's presentation and description of the center, Macdonald's formula, the Casselman-Shalika formula, and the Kato-Lusztig formula.
	www.math.umd.edu /~tjh (433 words)

	DLAP - Sparse Linear Algebra Package
		In solving a large sparse linear system Ax = b using an iterative method, it is not necessary to actually store the matrix A. Rather, what is needed is a procedure for multiplying the matrix A times a given vector y to obtain the matrix-vector product, Ay.
		CSPARSE is a library of C routines for direct methods of solving sparse linear systems.
		MGMRES is a FORTRAN90 routine which applies the restarted GMRES algorithm to solve a sparse linear system.
	www.csit.fsu.edu /~burkardt/f_src/dlap/dlap.html (3041 words)

	Matrices with Integer Entries (integer_matrix)
		The types integer_matrix and integer_vector together realize many functions of basic linear algebra.
		For example, if the linear system solver declares a linear system A x = b unsolvable it also returns a vector c such that c^T A = 0 and c^T b !=q 0.
		For example, if the linear system solver declares a linear system A x = b unsolvable it also returns a vector c such that c^T A = 0 and c^T b != 0.
	graphics.stanford.edu /courses/cs368/LEDA/node55.html (792 words)

	Matrices with Integer Entries ( integer_matrix )
		Most functions of linear algebra are checkable, i.e., the programs can be asked for a proof that their output is correct.
		If the system is solvable then (1/D)x is a solution, and the columns of spanning_vectors are a maximal set of linearly independent solutions to the corresponding homogeneous system.
		The implemenation follows a proposal of J. Edmonds (J. Edmonds, Systems of distinct representatives and linear algebra, Journal of Research of the Bureau of National Standards, (B), 71, 241 - 245).
	www.cs.cmu.edu /~smonti/html/leda/integer_matrix.html (749 words)

	How do I link to a BLAS or LAPACK library on the Linux cluster?
		Using the -static flag takes the memory space that would otherwise be used for.so shared libraries.
		For example, if the -static flag is not used, then dimensioning 3 1K by 1K double precision matrices requiring a total of 24 MBytes of storage would result in a run time (segmentation fault) message.
		Using the -static flag takes the memory space that would otherwise be used for.so shared libraries, so is not compatible with using shared libraries.
	www.ncsu.edu /itd/hpc/Documents/linuxblas.php (979 words)

	Alexander GIVENTAL's Home Page (Site not responding. Last check: 2007-10-25)
		Please visit Sumizdat Home Page, examine the book, and if you like it, make a link from your website to www.sumizdat.org in order to bring the book closer to students and their teachers.
		Linear algebra and differential equations Published by AMS
		Quantum cohomology of flag manifolds and Toda lattices (with Bumsig Kim)
	math.berkeley.edu /~giventh (188 words)

	Bernd Sturmfels \| U.C. Berkeley Mathematics (Site not responding. Last check: 2007-10-25)
		This point is illustrated by a snapshot of four recent contributions from biology to geometry, combinatorics and algebra.
		Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics.
		The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals and their polyhedral resolutions, to hands-on tools for studying algebraic varieties with group actions, such as toric varieties, flag varieties, quiver loci, and Hilbert schemes.
	math.berkeley.edu /~bernd (269 words)

	Linear Algebra (Site not responding. Last check: 2007-10-25)
		To extend the students knowledge of linear algebra, including vector spaces.
		Linear transformations from Rn to Rm and their representing matrices.
		Fraleigh, J.B. and Beauregard, R.A., Linear Algebra, Addison Wesley, 1986, 20 1526 751, Y
	www.tech.port.ac.uk /tud/db2002/UnivPort/level_2/MTH211.htm (171 words)

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