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	Block matrix - Wikipedia, the free encyclopedia
		In the mathematical discipline of matrix theory, a block matrix or a partitioned matrix is a partition of a matrix into rectangular smaller matrices called blocks.
		A block diagonal matrix is a block matrix which is a square matrix, and having main diagonal blocks square matrices, such that the off-diagonal blocks are zero matrices.
		In linear algebra terms, the use of a block matrix corresponds to having a linear mapping thought of in terms of corresponding 'bunches' of basis vectors.
	en.wikipedia.org /wiki/Block_matrix (405 words)

	Block - Wikipedia, the free encyclopedia
		A block (music) is a separate complete unit that is primarily not developed but instead used in various combinations, these may be contrasted or transformed, and each block may be broken into parts and developed independently.
		In sailing, a block is a pulley or a number of pulleys enclosed in sheaves so as to be fixed to the end of a line or to a spar or surface.
		Blocks (a) are separated by interblock gaps, (b) are delimited by an end-of-block signal, and (c) may contain one or more records.
	en.wikipedia.org /wiki/Block (541 words)

	Block matrix -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		A block diagonal matrix is a block matrix which is a square matrix, and having (The diagonal of a square matrix running from the upper left entry to the lower right entry) main diagonal blocks square matrices, such that the off-diagonal blocks are zero matrices.
		That again matches the idea of having distinguished (A union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets) direct sum decompositions of the (Territory over which rule or control is exercised) domain and (A series of hills or mountains) range.
		In that case, for example, the (An oblique line of squares of the same color on a checkerboard) diagonal blocks in the obvious sense are all square.
	www.absoluteastronomy.com /encyclopedia/b/bl/block_matrix.htm (389 words)

	PlanetMath: partitioned matrix (Site not responding. Last check: 2007-11-07)
		A partitioned matrix, or a block matrix, is a matrix
		are matrices of the same dimension partitioned into identially-sized blocks, the partition of the sum is the sum of the partitions.
		This is version 6 of partitioned matrix, born on 2003-04-04, modified 2004-08-24.
	planetmath.org /encyclopedia/PartitionedMatrix.html (133 words)

	[No title]
		We did notice that by increasing the tiling size to larger blocks, we were able to stop some of the performance degradation on the larger-sized matrices.
		If the dimensions of matrix C are not a multiple of the tiling size, then the result of the computation is stored in a buffer.
		At the end of the matrix multiplication, the matrix is copied back to C. The advantage of this method is that no additional fringe handling matrix multiply code needs to be generated.
	www.cs.berkeley.edu /~ejr/GSI/cs267-s04/homework-1-results/SS/hw1.htm (1662 words)

	Simulink and the DSP Blockset (DSP Blockset) (Site not responding. Last check: 2007-11-07)
		In general, any Matrix size setting in the Matrix To Workspace block that corresponds to a matrix with a total of 12 elements is allowable.
		Because the matrix dimension is determined by the parameter setting in the individual receiving block, it is important to track the dimensions of matrix inputs and outputs.
		A scalar input is a 1-by-1 matrix, and a length-N vector input is either a 1-by-N or N-by-1 matrix, depending on the input dimensions you enter in the block's matrix size parameter.
	www.tau.ac.il /cc/pages/docs/matlab/help/toolbox/dspblks/dspg21.html (390 words)

	Guide and Reference
		The process grid definition and array descriptor are used to establish the mapping between the global vector or matrix and its corresponding process and distributed memory location.
		Throughout this book, the _ (underscore) symbol in the array descriptor is followed by an X to indicate a vector or an A to indicate a matrix.
		After a global vector or matrix is block-cyclically distributed over a process grid, you may decide to use only a portion of the global data structure.
	www.umiacs.umd.edu /~jhu/DOCS/SP/docs/pessl/pessl066.html (670 words)

	Block algorithms: Matrix Multiplication as an Example
		Typically an algorithm that refers to individual elements is replaced by one that operates on subarrays of data, which are called blocks in the matrix computing field.
		The advantage of this approach is that the small blocks can be moved into the fast local memory and their elements can then be repeatedly used.
		Blocking introduces block size parameters that have nothing to do with the problem being solved and which must be adjusted for each computer and each algorithm if good performance is to be achieved.
	www.netlib.org /utk/papers/autoblock/node2.html (611 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		The standard Taylor's series expansion uses powers of the K matrix whereas an alternative block-matrix representation of K and its powers exploits the symmetry that is present in the matrix EXP(K).
		Let m be the dimension of the smaller null block of K and let n be the dimension of its larger null block.
		The matrix approximation to EXP(K) employed in SCF minimizations should be accurately orthogonal as well as appropriately close to the exponential value.
	www.emsl.pnl.gov /proj/tms/hpcc_actinides/research-98/argonne/Pade.html (479 words)

	Similarity over C
		where [c] is a 1 by 1 block, B is a 1 by n-1 block, 0 denotes an n-1 by 1 block, and D is an n-1 by n-1 block.
		Thus, every matrix is similar to a matrix in Jordan form, and two matrices in Jordan form are similar if and only if they have the same blocks, although not necessarily arranged in the same order.
		One can write a matrix in Jordan form as the sum of a diagonal matrix D with the same diagonal entries, and an upper triangular matrix N with all 0's on the diagonal.
	www.math.lsa.umich.edu /~hochster/419/cxsim.html (1175 words)

	[No title]
		The maximum entropy extension of a banded matrix with bandwidth bw is defined to be an extension that causes the inverse of the extended matrix to be banded with a bandwidth bw as well.
		However, if M1 is extended to a matrix M1ext by changing the zero entries outside the band such that the inverse of M1ext is banded with the same bandwidth as M1, then the M1ext is known as the extension of M1 matrix in the maximum entropy sense.
		The matrix B is known as the Schur’s complement.
	www.bridgeport.edu /~dichter/papers/entropy_pap1.1.doc (1579 words)

	Block Diagonal Matrix (Site not responding. Last check: 2007-11-07)
		You may have noticed that every matrix is block diagonal, consisting of one block running from 1 to n.
		Let the first block, in the upper left, be defined by the interval [1,j].
		As a check, apply this result to a diagonal matrix, where each block is a single element.
	www.mathreference.com /la-jf,bdiag.html (391 words)

	GNU Scientific Library -- Reference Manual: Matrices
		The physical memory layout of the matrix begins in the top left hand-corner and proceeds from left to right along each row in turn.
		stores the location of the memory block in which the elements of the matrix are located (if any).
		field is set to one and the block will be deallocated when the matrix is freed.
	linux.duke.edu /~mstenner/free-docs/gsl-ref-1.0/gsl-ref_163.html (353 words)

	Partitioning a Matrix into a Block Matrix
		(Note: the second parameter is the number of rows of the upper left hand and the third parameter is the number of columns of the upper left hand block.
		We use the ValueOf function to associate the value of the block to the block without actually assigning it.
		The BlockQ command tells the user if the variable represents a block matrix and is assigned within PartitionMatrix via the SetBlock command.
	math.ucsd.edu /~ncalg/NCBIGDOC02/node62.html (277 words)

	John Halleck's Block Matrix Givens Rotation
		If you are one of the few people in the world that have been here before, note that there have been some changes in the presentation and form.
		It is the same matrix and transformation, but now in a form that is easier for other proofs (still to come on the web site) can be made.
		The cooresponding Householder matrix is, of course, Has no non-zero elements if Y has none.
	www.cc.utah.edu /~nahaj/math/blockgivens.html (698 words)

	BLIMPS
		matrix: score a block or matrix against a database of sequences
		To score a block query against a database of sequences, specify the block file name and the sequence database name.
		You can produce a matrix file by asking to export matricies to a file, only when action is to score a block query against a database of sequences (matrix).
	bioweb.pasteur.fr /seqanal/interfaces/blimps.html (556 words)

	NICONET Task I.B (Site not responding. Last check: 2007-11-07)
		Only the first block row, or the first block column of the Toeplitz matrix must be given.
		The Toeplitz matrix could be defined by either its first block row, or its first block column.
		The coefficient matrices are nxk-by-nxk symmetric block Toeplitz matrices BT, with k taking values in [1 2 20 30], and n obtained by dividing 300 to k, hence nxk = 300 ; k is the blocksize, and n is the number of the blocks.
	www.win.tue.nl /niconet/NIC2/NICtaskIB.html (1302 words)

	Block Matrix Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-11-07)
		Looking For block matrix - Find block matrix and more at Lycos Search.
		Find block matrix - Your relevant result is a click away!
		Look for block matrix - Find block matrix at one of the best sites the Internet has to offer!
	www.artisticnudity.com /encyclopedia/Block_matrix (550 words)

	A Randomizing Butterfly Transformation Useful in Block Matrix Computations - Parker (ResearchIndex)
		...block submatrix of the RBT e A is nonsingular.
		It is not difficult to show that this polynomial, which has a finite number of zeroes, is nonzero with probability 1.
		In a variation of the RBT approach is presented that is well suited to block matrix computations.
	citeseer.ist.psu.edu /189177.html (655 words)

	[NMusers] Fixed elements within a block covariance matrix (Site not responding. Last check: 2007-11-07)
		Ken _______________________________________________________ From: vgcasabo - vicente.casabo@uv.es Subject: RE: [NMusers] Fixed elements within a block covariance matrix Date: 1/13/2004 11:29 AM Hi, all I do not understand, that if X11 is correlated with X33, and X22 is correlated with X33, X11 and X22 are not correlated.
		I think that as long as the matrix is positive definite it will work.
		However, the elements in the BAND matrix must, of course, be symmetrical.
	www.cognigencorp.com /nonmem/nm/99jan012004.html (1285 words)

	Forum -> How to use a sanding block for matrix
		I've read a few posts lately that tinters stay away from the sanding block because it's flat and the window is curved, thus not giving good contact.
		The majority of the dot matrix is on the flat end of the glass while the ends might get a little curved so once I reach the edges, I use the tip of the sanding block to sand the last 1" or so of the dots.
		When you come towards the edge of the glass where the dot matrix is, you simply use the end of the block for the contact...the "body" of the "contoured" block is used for the body of the matrix...I've done hundreds of matrix on cars with it...has never failed me
	www.tintdude.com /forum/index.php?showtopic=13299 (943 words)

	Block matrix decompositions
		In fact, mostly the entire theory of recursive algorithms for autoregressive modeling comes from these block matrix results.
		Note that to reverse the action of adding a multiple of one equation to another, we subtract that multiple.
		Matrix inversion lemma An important result comes by equating block elements of the two inversion formulas, e.g:
	ccrma-www.stanford.edu /~jos/lattice/Block_matrix_decompositions.html (232 words)

	NICONET Task I.B (Site not responding. Last check: 2007-11-07)
		In addition, routines for QR factorization of general (block) Toeplitz matrices, and for solving associated linear systems in a least squares sense are available.
		Only the first block row, and/or the first block column of the Toeplitz matrix must be given.
		The Fortran routines for TASK I.B are aimed to perform efficiently and reliably factorizations of structured matrices, specifically, block Toeplitz matrices, and solve the associated linear matrix equations, using structure-exploiting algorithms.
	www.win.tue.nl /niconet/NIC2/NICtask1B.html (1541 words)

	Block Matrix Manipulation
		By block matrices we mean matrices with noncommuting entries.
		As of NCAlgebra version 3.2 one can handle block matrix manipulation two different ways.
		One is the old way as described below where you use the command MatMult[A, B] to multiply block matrices A and B and tpMat[A] to take transposes.
	math.ucsd.edu /~ncalg/NCBIGDOC02/node55.html (128 words)

	BLIMPS
		BLIMPS : score a block or matrix against a database of sequences (Wallace & Henikoff)
		The same as clustering except that the weights of the sequences are taken explicitly from the given weights, rather than implicitly from the clustering.
		If you give a block file, Blimps converts it to a position-specific scoring matrix; but you can directly give a matrix file you have one (see conversion parameter).
	bioweb.pasteur.fr /seqanal/interfaces/blimps_matrix.html (493 words)

	Strassen's Method for Matrix-Multiplication
		C22 in Step 2 achieves the goal of obtaining the product matrix C via Strassen's Method, but this recursive method incurs one less matrix multiplication in each recursion than the original one suggested.
		The standard way to implement a matrix in C is as a vector of pointers to vectors of data (doubles in our case).
		The other approach requires allocation of one contiguous block of memory to house all the data: such a large allocation may be unavailable, due to fragmentation.
	www.prairienet.org /~sjmccaug/Strassen.htm (1676 words)

	ipedia.com: Block Article (Site not responding. Last check: 2007-11-07)
		The concept of a block as a group or a piece appears in various fields: A city block is the smallest part of a town enclosed by streets.
		Railway are divided into blocks guarded by combinations of sign...
		In programming languages, a block (progamming) forms a subdivision of a program that serves to group related statements, delimit routines, specify storage allocation, delineate the applicability of labels, or segment parts of the program for other purposes.
	www.ipedia.com /block.html (394 words)

	CAAM 520 Assignment 5 (Site not responding. Last check: 2007-11-07)
		Implement the parallel matrix multiply algorithm (Fox's algorithm) in Pacheco chapter 7.
		Output format for the matrix is the same as the input format above
		The output of the routine is a single matrix that solves the block diagonal system of equations, in the same format as input matrices, shown here
	www.caam.rice.edu /~caam520/Assignments/a5.html (215 words)

	Languages and Implementation Techniques for Block-structured Matrix Computations (Site not responding. Last check: 2007-11-07)
		The aim of this project is to design and implement a programming language for matrix and PDE grid computations, with special support for block-structured algorithms.
		A specific goal is to achieve "performance portability", which means it should be able to be compile the programs for different architectures with good and predictable performance.
		· a limited nondeterminism in some operations for matrix and grid decomposition, allowing the compiler to choose block sizes to fit the memory parameters of the machine at hand, and
	www.it.kth.se /forskningsprojekt-detalj.html?projektid=42 (252 words)

	Block Arnoldi Reductions
		Algorithm 7.11 lists an algorithm to compute a block Arnoldi reduction.
		375] (for symmetric matrices) and is the one used by the implicitly restarted block Lanczos code [
		The advantage is that steps (3)-(5) reduce the cost of I/O by a factor of the block size and increase the amount of floating point operations per memory reference.
	www.cs.utk.edu /~dongarra/etemplates/node236.html (305 words)

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