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Topic: Normal matrix

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	The Twisted Matrix: Dream, Simulation or Hybrid?
		Normal sensory input is blocked, attentional capacities are impaired or lost, memory is distorted, reasoning and logic are weakened, narratives run wild, self-reflection is dampened or destroyed, emotion and instinct are hyperstimulated, and forms of ‘top-down’ willed control and decision-making diluted and easily overwhelmed.
		Normal wakefulness is characterized by high activation (as measured by EEG for example) corresponding to fairly intense experience, external input sources (the brain is receiving and processing a rich stream of sensory signals from the world, rather than being shut down and largely re-cycling its own activity), and a distinctive mode.
		The typical matrixer does not display the full cognitive signature of uncritical dreaming, and it therefore seems unlikely that the machines are actively maintaining the brains of their human power cells in the standard (aminergic-off, hyper-cholinergic) REM-sleep mode.
	whatisthematrix.warnerbros.com /rl_cmp/new_phil_clark.html (7208 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		The normal vector is rescaled after it is multiplied by the inverse modelview matrix and before it is normalized.
		Normals are of interest only in eye coordinates, so the rules governing their transformation to other coordinate systems are not examined.
		Normals which have unit length when sent to the GL, have their length changed by the inverse of the scaling factor after transformation by the model-view inverse matrix when the model-view matrix represents a uniform scale.
	oss.sgi.com /projects/ogl-sample/registry/EXT/rescale_normal.txt (358 words)

	Encyclopedia: Game theory (Site not responding. Last check: 2007-11-06)
		The normal or strategic form game is a matrix which shows the players, strategies, and payoffs (see the example to the right).
		When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other.
		Normal form is used to represent simultaneous games and extensive form is used to represent sequential ones.
	www.nationmaster.com /encyclopedia/Game-theory (7009 words)

	Treating Osteoarthritis with Chondroprotective Agents
		Normal articular cartilage is composed of chondrocytes that occupy approximately 5% of the tissue volume, and the extracellular matrix, which composes the remaining 95% of the tissue.
		The chondrocytes secrete and maintain the matrix; the matrix in turn supplies the chondrocytes with an environment conducive to their continued existence in the face of a high level of mechanical stress.
		Since the molecular structure of the matrix determines both the rate of diffusion as well as the nature of diffusible particles, normal matrix is also a prerequisite for chondrocyte survival.
	www.aboutjoints.com /physicianinfo/topics/osteoarthritisknee/chondro.htm (3214 words)

	Linear Algebra
		For this matrix A, we have Vl < = Vr >tr = V, where Vl is the left null-space of A, Vr is the right null-space of A, and V is the null-space of D -- the diagonal in the factorization of the matrix A, as A = < D >.
		Definition: Given a matrix A and an arbitrary non-singular matrix B. The product (B A Binv) is called the generalized similarity transformation of the matrix A by B. Theorem: If B is an ortho-normal (or unitary) matrix O; the generalized similarity transformation reduces to the similarity transformation.
		For an n by n matrix, the degree of this characteristic polynomial is n.
	www.rism.com /LinAlg/real.htm (3862 words)

	neqfile.html - 96Dec26
		Rows of the reduced normal equation elements for this data set for which a final solution based on the final global solution is desired.
		The rows of the normal equation matrix for these parameters are first forward reduced and are saved in that state in the type 7 records of this file.
		These follow the local parameters in the normal equation matrix and after the local parameters have been forwarded reduced the rows of the normal equation matrix holding the global parameters are saved in the type 8 records of this file.
	www.ngs.noaa.gov /GRD/GPS/DOC/gpscom/neqfile.html (2442 words)

	RX-7 Owners Club - normal to matrix? (Site not responding. Last check: 2007-11-06)
		recently i dont a coarse tuning on the normal mode and the afr for idle is always around 12.50 to 13.0 and cruising 13 ish.
		Matrix mode allows for a fine tunning at any given RPM and Vacuum (or boost).
		If the car is dying in when idleing in "normal" mode and you have afr's 14.5-15, you need to add more gas (assuming everything else is OK (i.e.
	www.rx7club.com /showthread.php?t=403916 (281 words)

	Science News Online - This Week - Feature Article - 8/30/97 (Site not responding. Last check: 2007-11-06)
		Cells in the breast normally secrete this protein during involution, the remodeling of the extracellular matrix that occurs after pregnancy, when the breast becomes smaller and stops making milk.
		To create their cancer cells, the investigators grew normal mammary cells without the aid of the chemical growth factors ordinarily present in the cell culture medium.
		The most important aspect of the extracellular matrix research by Bissell's group, contends Vogelstein, is its attempt to study cancer in an environment similar to that of tumor cells in the body.
	www.sciencenews.org /pages/sn_arc97/8_30_97/bob2.htm (1949 words)

	John Halleck's
		The usual arguments against Normal Equations is that the condition number of the normal equation matrix is the square of the condition number of the original problem.
		This is not normally much of an issue in practice, since the matrix in the survey case is not only positive definite, but is very close to being diagonally dominate.
		Since the matrix is then almost in the form that R needs to be in the QR factorizations, the amount of work needed to complete the task is low.
	www.cc.utah.edu /~nahaj/cave/survey/intro/orthogonalization.html (760 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		This sort of field in a matrix calculator is very useful in projective geometry, although it is not standard because no fractions, and therefore no division, exist.
		If there is not enough input data to fill the matrix with the specified dimensions, then the matrix is invalid, and none of the data for that matrix will be read.
		The matrix has 4 fields - row and col dimensions, a name for ease of use, and a ptr to a two dimensional array of the proper dimensions.
	www.people.fas.harvard.edu /~dpopper/fpc/manual.txt (1722 words)

	Matrix C++ template class library with full source code
		Matrix TCL Pro is a matrix template class library for performing matrix algebra calculations in C++ programs in easy and efficient manner for engineering / scientific works.
		It supports most of the matrix algebra operations and enables programmers to use matrix object just like other built-in data types in their C++ programs.
		This is a normal dense matrix algebra library.
	www.techsoftpl.com /matrix (189 words)

	Sparce Matrix Method
		This knowledge allows one to calculate the normal matrix as a sparse matrix, the vast majority of the off-diagonal elements are never calculated or even have computer memory allocated for their storage.
		Even with the simplification of the normal matrix introduced by the sparse approximation the problem of inverting the matrix is difficult.
		[2] uses the sparse matrix approximation to the normal matrix.
	www.uoxray.uoregon.edu /dale/papers/CCP4_1994/node6.html (536 words)

	[No title]
		Normals, however, are transformed by the inverse transpose of the modelview matrix.
		In addition, a current normal, current texture coordinates, current color, current matrix indices, and current weights may be used in processing each vertex.
		Normals are used by the GL in lighting calculations; the current normal is a three- dimensional vector that may be set by sending three coordinates that specify it.
	oss.sgi.com /projects/ogl-sample/registry/ARB/matrix_palette.txt (2006 words)

	No Title
		matrix inversions are done using in-place Cholesky methods where possible: it is for standard use the fastest, least memory consuming and a stable method.
		is calculated by backsubstitution of the identity matrix, and the uncertainties by (22).
		The covariance matrix should be calculated by doing a final linear run on the residuals, and solve the equations.
	www.atnf.csiro.au /people/wim.brouw/blsq/blsq.html (1555 words)

	Dealing With Larger Networks
		For example if the size of the normal matrix is doubled, the time taken to solve the normal equations is increased by a factor of 8.
		There are certain algorithms for inverting a matrix (for example the Cholesky decomposition) that allow a large number of the zero terms to be ignored in the computation of the matrix inverse.
		The matrix may not be sparse enough to be worth the computation effort of re-organising the order of the parameters - there is some cost in optimizing the order of the parameters in x.
	www.sli.unimelb.edu.au /nicole/surveynetworks/02a/notes11_01.html (854 words)

	ipedia.com: Probability distribution Article (Site not responding. Last check: 2007-11-06)
		The F-distribution, which is the distribution of the ratio of two normally distributed random variables, used in the analysis of variance.
		The normal distribution, also called the Gaussian or the bell curve.
		It is ubiquitous in nature and statistics due to the central limit theorem: every variable that can be modelled as a sum of many small independent variables is approximately normal.
	www.ipedia.com /probability_distribution.html (1030 words)

	Matrix Market: Glossary
		A matrix is diagonally dominant if the absolute value of each diagonal element is greater than the sum of the absolute values of the other elements in its row (or column).
		A Hessenberg matrix is `almost' triangular, that is, it is (upper or lower) triangular with one additional off-diagonal band (immediately adjacent to the main diagonal).
		The Jordan normal form of a matrix is a block diagonal form where the blocks are Jordan blocks.
	math.nist.gov /MatrixMarket/glossary.html (756 words)

	Normal matrix -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		A ((psychoanalysis) a combination of emotions and impulses that have been rejected from awareness but still influence a person's behavior) complex square (A rectangular array of elements (or entries) set out by rows and columns) matrix A is a normal matrix (Click link for more info and facts about iff) iff
		Phrased differently: a matrix is normal if and only if its (Click link for more info and facts about eigenspace) eigenspaces span C
		The concept of normal matrices can be generalized to (Click link for more info and facts about normal operator) normal operators on (A metric space that is linear and complete and (usually) infinite-dimensional) Hilbert spaces and to normal elements in (Click link for more info and facts about C-star algebra) C-star algebras.
	www.absoluteastronomy.com /encyclopedia/n/no/normal_matrix.htm (388 words)

	Shading Language Extensions
		Normals are transformed such that they remain perpendicular to a plane undergoing the same transformation.
		Casting from a float to a matrix results in a matrix with all zeros except on the diagonal, where all four values equal the original float.
		Dividing by a matrix is equivalent to multiplying the left hand matrix by the inverse of the right hand matrix.
	www.dotcsw.com /doc/slext.html (3841 words)

	CNW Group (Site not responding. Last check: 2007-11-06)
		This normal course issuer bid is intended to commence on March 3, 2005 and will terminate on March 2, 2006.
		In accordance with the Declaration of Trust by which MATRIX is governed, market purchases pursuant to its normal course issuer bid may be effected by the Fund.
		MATRIX may, during the 12 month period commencing March 3, 2005 purchase on the TSX up to 2,988,410 units, being 10% of the public float of the units.
	www.newswire.ca /releases/March2005/01/c9903.html (245 words)

	Matrix Diagonalization
		is a Jordan block or Jordan box, and the matrix J is called a Jordan canonical form or Jordan normal form of the matrix A.
		The diagonal elements of the diagonal matrix D similar to the matrix A are the eigenvalues of the matrix A.
		In general case of the diagonalization of a matrix one must confine himself to the Jordan normal form (1).
	www.cs.ut.ee /~toomas_l/linalg/lin2/node19.html (281 words)

	Multivariate Normal Random Numbers
		To generate an NxP matrix of normal random numbers in Dataplot, you must specify a Px1 mean vector and a PxP variance-covariance matrix.
		The diagonal of the variance-covariance matrix specifies the scale parameters of the P columns.
		Dataplot generates multivariate normal random numbers with a mean vector AMU and a variance-covariance matrix SIGMA using the RDMNOR routine written by Charlie Reeves while he was a member of the NIST Statistical Engineering Division.
	www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/mvnran.htm (432 words)

	Least Squares Network Adjustments via QR Factorization
		The condition number of the matrix is a measure of the amount of significance lost when you solve the system it represents.
		The traditional method is to use a Cholesky factorization of the matrix on the left-hand side into an upper triangular matrix R and its transpose.
		The upper triangular part of the matrix R that comes out of this factorization is the same matrix that would have come out of the Cholesky factorization in the normal equation case.
	www.cc.utah.edu /~nahaj/survey/QRintro.html (6874 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		As of now //this code is in a very basic state and only supports the calculation //of a normal vector, given three points defining a plane.
		Once the two direction vectors are calculated, they are used to define a surface //and it's normal vector is calculated using a cross-product.
		The return value is a matrix //containing the normal vector.
	www.ccs.neu.edu /home/gtryd/MatrixStuff.java (356 words)

	Globals:
		The flat normal prior is uniform within the unit square and dropping outside the square according to the normal distribution.
		However, fundamental progress remains to be made on methods of integrating the bivariate normal, as all currently available methods are innacurate and jump discontinuously and for very small values.
		In practice, this procedure is useful for ensuring that a positive definite variance matrix can be found due to numerical, rather than theoretical or empirical, difficulties, as can happen when the mode of the truncated normal is far from the unit square due to imprecision in the function that computes the bivariate normal CDF.
	gking.harvard.edu /ei/node15.html (1573 words)

	MR Imaging of Normal and Matrix-depleted Cartilage: Correlation with Biomechanical Function and Biochemical Composition ...
		MR Imaging of Normal and Matrix-depleted Cartilage: Correlation with Biomechanical Function and Biochemical Composition -- Wayne et al.
		Twelve normal porcine knees were obtained from a local slaughterhouse.
		Although both chondroitinase treatment (white bars) and collagenase treatment (gray bars) caused increases in these imaging parameters from the normal levels, a difference between the two treatments in terms of resulting T2 was evident.
	radiology.rsnajnls.org /cgi/content/full/228/2/493 (4195 words)

	Every Normal Toeplitz Matrix is Either of Type I or Type II
		Every Normal Toeplitz Matrix is Either of Type I or Type II : SIAM Journal on Matrix Analysis Vol.
		In their 1995 manuscript, Farenick and Lee proved that every normal Toeplitz matrix of order less than or equal to 5 is either of type I or of type II and had left open the case of higher order as a conjecture.
		Since the idea of proof in the work just mentioned is somewhat different from the one of this paper, the editor has recommended that the author publish in a separate paper.
	epubs.siam.org /sam-bin/dbq/article/29315 (172 words)

	Reflections : oblique frustum clipping - GameDev.Net Discussion Forums (Site not responding. Last check: 2007-11-06)
		Intrestingly, if I set up the reflection matrix first and then adjust the projection matrix I do kinda get a result, however its a faded version of the ZY plane reflection, which is rotating backwards to my main object, and my XZ plane is still empty.
		Not had a chance to check my maths yet, its just odd that the det M (of the 3x3 matrix) comes out as 0 when the matrix is definately invertable, so unless there is a typo in the book the only other answer is i've had a brain fart while coding up that bit.
		The normal of that plane, PN, is defined as (A,B,C) => PN = (0, 0, 1).
	www.gamedev.net /community/forums/viewreply.asp?ID=1597068 (2031 words)

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