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Topic: Transformation matrix

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Linear transformation

List of matrices

Hadamard gate

Distance matrix

Eigenvalue

Spectral theorem

Spectrum of an operator

Eigenplane

Halting problem

3D computer graphics

Feast of Tabernacles

Clique problem

Homological algebra

Standard Model

List of group theory topics

	senocular.com Tutorial: Understanding the Transformation Matrix in Flash 8 page 1
		In the Matrix class in Flash, u,v, and w are not accessible as properties as a, b, c, d, tx, and ty are.
		With matrix multiplication, however, it is required that the first matrix in the operation have a number of columns equal to the number of rows in the second matrix.
		In matrix multiplication, the resulting matrix is an m x n matrix where m is the number of rows in the first matrix and n is the number of columns in the second.
	www.senocular.com /flash/tutorials/transformmatrix (6279 words)

	Transformation matrix - Wikipedia, the free encyclopedia
		If one has a linear transformation T(x) in functional form, it is easy to determine the transformation matrix A by simply transforming each of the vectors of the standard basis by T and then inserting the results into the columns of a matrix.
		A consequence of the ability to compose transformations by multiplying their matrices is that transformations can also be inverted by simply inverting their matrices.
		All ordinary linear transformations can be converted into affine transformations by expanding their matrices by one row and column, filling the extra space with zeros except for the lower-right corner, which must be set to 1.
	en.wikipedia.org /wiki/Transformation_matrix (1041 words)

	GameDev.net - Matrix Transformation
		Matrix Multiplication There are two matrix operations which we will use in our matrix transformations, multiplying (concatenating) two matrices, and transforming a vector by a matrix.
		Matrix multiplication is the operation by which one matrix is transformed by another.
		As far as matrix transformations are concerned, consider an arm as an example of a hierarchical object.
	www.gamedev.net /reference/articles/article417.asp (4243 words)

	Color Transformation and the Color Matrix (Site not responding. Last check: 2007-11-03)
		The element of the fifth row and the fifth column of the matrix must be 1 and all of the other entries in the five columns must be 0.
		For example, the matrix shown in Figure 10-20 doubles the intensity of the red component, decreases the intensity of the green component by half, triples the intensity of the blue component, and decreases the opacity of the color by half (semi-transparent).
		The Matrix class is used in general transformation to transform graphics shapes and images, while the ColorMatrix class is specifically designed to transform colors.
	www.c-sharpcorner.com /Code/2004/April/Transformations05.asp (1623 words)

	Matrix (flash.geom.Matrix) -- Version 8
		Returns a new Matrix object that is a clone of this matrix, with an exact copy of the contained object.
		Sets each matrix property to a value that cause a transformed movie clip or geometric construct to be identical to the original.
		Modifies a Matrix object so that the effect of its transformation is to move an object along the x and y axes.
	livedocs.macromedia.com /flash/8/main/00002389.html (706 words)

	SetColorMatrix. Set color transformation matrix. Image.
		A transformation consisting of a linear transformation followed by a translation is called an affine transformation.
		A 5x5 matrix that represents an affine transformation is called a homogeneous matrix for a 4-space transformation.
		The element in the fifth row and fifth column of a 5x5 homogeneous matrix must be 1, and all of the other entries in the fifth column.
	www.asppainter.com /methods/SetColorMatrix.html (124 words)

	Affine Transformations
		The transformations that move lines into lines, while preserving their intersection properties, are special and interesting, because they will move all polylines into polylines and all polygons into polygons.
		Evidently coefficients A, B, D, and E determine a linear transformation and coefficients C and F determine a parallel translation: that is, such three-by-three matrices describe affine two-dimensional transformations.
		Recall that, for a linear transformation, the first column of the matrix contains the coefficients of the point where the first basis vector (1, 0) is sent and the second column contains the coefficients of the point where the second basis vector (0, 1) is sent.
	www.quantdec.com /GIS/affine.htm (3073 words)

	Transformation Data Records
		The transformation data set is used to define these transformations via a transformation matrix.
		The matrix is stored such that terms 1,2,3,5,6,7,9,10, and 11 are rotation terms, term 13 is shift in x, term 14 is shift in y, term 15 is shift in z, and term 16 is the scale term.
		The compound matrix may be determined by expressing the compound transformation as a combination of the five simple transformations given above.
	www.princeton.edu /~dynaflow/femgv/manuals/appends/node27.htm (359 words)

	Linear transformations (Site not responding. Last check: 2007-11-03)
		Criterion for the linearity of a transformation of V
		Matrix of a linear transformation with respect to a basis in V. Null-space of a linear transformation
		It can easily be proved that t+t' is a linear transformation and that the matrix of t+t' is equal to the sum of the matrices of t and of t'.
	www.ping.be /~ping1339/lintf.htm (2183 words)

	Coordinate Systems, Transformations and Units - SVG 1.1 - 20030114
		Transformations can be nested, in which case the effect of the transformations are cumulative.
		The result of this transformation is that the coordinate (30,30) in the new user coordinate system gets mapped to coordinate (80,80) in the original coordinate system (i.e., the coordinates have been translated by 50 units in X and 50 units in Y).
		Note that the transform attribute on the 'CoordinateReferenceSystem' does not indicate that a transformation should be applied to the data within the file, it simply describes the transformation that was applied to the data when being encoded in SVG.
	www.w3.org /TR/SVG/coords.html (7070 words)

	Transformation of coordinates (Projective; Affine; Metric) (Site not responding. Last check: 2007-11-03)
		Since these two vectors are linear independent the determinant of the transformation matrix M is not zero and so the transformation matrix M is not singular.
		The metric transformations are a subset of the affine transformations.
		If M is a regular matrix such that the permutation preserves the distance of two regular points, then M is the matrix of a metric transformation.
	www.ping.be /~ping1339/coortf.htm (1901 words)

	CS405 Lab 3: Matrix Transformation
		In general, a new transformation matrix is always concatenated to the global matrix from the right.
		The first replaces the current matrix with the identity matrix, and the next two commands are used to push and pop the current matrix.
		Popping a matrix replaces the current matrix with the matrix on the top of the stack and removes that matrix from the stack.
	www.cs.uregina.ca /Links/class-info/405/WWW/Lab3 (2572 words)

	Margaret Sinclair: Linear transformations using spreadsheets
		This unit investigates the effect of a variety of linear transformations on a unit square and a rectangle.
		Students record their observations in a table and conjecture relationships between characteristics of the transformation matrix and the shape, orientation and area of the image.
		If the linear transformation is an isometry, then the lengths of vectors and angles betweeen vectors remain unchanged under the transformation.
	mathforum.org /workshops/sum98/participants/sinclair/outline.html (541 words)

	rigid body transformations
		This homogenous coordinate transformation matrix shifts the origin from (0,0,0) to the exact center of the standard file.
		Coordinate units are modified by this homogenous coordinate transformation matrix to be equivalent to those used in an interpolated version of the reslice file.
		If your alternative package generates a linear algebraic transformation matrix of its own, don't forget that transformation matrices are dependent upon the coordinate system used and that the AIR internal coordinate system used to define transformation matrices may differ from that of your alternative package.
	bishopw.loni.ucla.edu /AIR5/rigidbody.html (912 words)

	ASC Coordinate Transformation-The Pixlib Library
		Transformation calculations are performed by matrix-representation routines for maximum flexibility.
		The line arrows connecting a pair of coordinate systems indicate the coordinate transformation is both forward and backward, and the aim of the transformation is explained at the side.
		For instance, transformation of CPC to LSI is to account for chip orientation in space, and N to FP is to convert the 3-D HRMA nodal position to the 2-D pixel focal plane coordinates.
	www.adass.org /adass/proceedings/adass96/heh.html (1223 words)

	Is this a valid approach to decompose a transformation matrix with pivot points? - Numerical Recipes Forum
		A child is inheriting the transformations from the parent.
		The transformation is represented in the components as translation, scaling and rotation.
		The rotation and scaling is transformed with a scaling pivot and a rotation pivot.
	www.nr.com /forum/showthread.php?t=768 (404 words)

	Matrix Filter (Site not responding. Last check: 2007-11-03)
		Adjust the default matrix entries by the appropriate trigonometry function.
		Maximizing the effects available with the linear transform matrix requires a thorough understanding of linear algebra.
		Given an object with a Matrix filter applied, the object is rotated by the angle entered.
	msdn.microsoft.com /workshop/author/filter/reference/filters/matrix.asp (879 words)

	DRP's Effect Point and Transformation Matrix Tutorial - Atari Forums
		A transformation matrix is a way of taking values and inserting them into an equation to change the position of vertices.
		A matrix is a two dimensional array of numeric data, where each row or column consists of one or more numeric values.
		A matrix with M rows and N columns is defined as a MxN matrix.
	www.ataricommunity.com /forums/showthread.php?t=510820 (4409 words)

	Distributional Matrix Transformation
		The distributional matrix transformation problem was first shown to be complete for DistNP by Gurevich [Gur90] (see also [BG95]).
		integer matrix, it is decidable in polynomial time whether it represents a linear transformation.
		be the matrix with a single entry equal to 1 and all other entries zero.
	www.uncg.edu /mat/acc-forum/avgnp/node33.html (537 words)

	Chouser's "Transformation Matrix Sampler" Applet (Site not responding. Last check: 2007-11-03)
		The Transformation Matrix Sampler is made up of four classes, all of which communicate to produce the results seen here.
		Each of the algebraic expressions in the transformation matrix above is stored in an instance of this class.
		This is where mouse-movement is trapped and the transformation matrix is applied to the various points.
	bluweb.com /us/chouser/proj/java/transmat (278 words)

	New Transformation Equations and the Electric Field Four-vector
		A four-dimensional orthogonal transformation matrix is used as the starting point for the replacement of the Lorentz transformation equations, allowing the electric field to be described by a four-vector and forcing Maxwell's equations to include extra terms.
		It has become apparent to me that a set of transformation equations exist which replace the Lorentz equations while still satisfying the requirement that the space-time interval remains invariant under transformation.
		Contrary to the Lorentz transformation, there is a rotation of the y'-z' plane relative to the y-z plane.
	www.softcom.net /users/der555/original.html (1304 words)

	Matrices/Spreadsheets/Transformations
		Student will use the spreadsheet to answer specific questions on the worksheets, designed to teach students how matrix multiplication is related to geometric transformations.
		Students will be able to use a matrix to represent a 2 dimensional figure by labeling vertices.
		Students will be able to predict an image given a preimage and a matrix transformation.
	www.worldwebdynamics.com /lou/Matst.htm (622 words)

	Householder Transformation Method
		Householder's method is used to construct a similar symmetric tridiagonal matrix.
		The second Householder transformation is applied to the matrix
		This program will be harder to read, but might prove to be more efficient when the size of the matrix is larger.
	math.fullerton.edu /mathews/n2003/HouseholderMod.html (358 words)

	transformation matrix
		The transformation matrix is an array of numbers describing the transformation of a given ST_Spatial.
		By inserting values into the matrix, you can specify how all x, y, or z coordinates will be manipulated.
		All transformations can be peformed at the same time, but it is not necessary to do all three.
	www.alexandria.ucsb.edu /~zheng/informix/SW30UG/t-matrix.htm (144 words)

	[No title]
		Students investigate the connection between geometric transformations and matrix multiplication.
		By entering the coordinates of the vertices of a geometric figure into a matrix and then multiplying by a 2x2 diagonal matrix, they analyze the correspondence between the multiplier matrix and the transformation it produces on the vertices of the figure.
		Students then formulate a general rule relating the elements of the multiplier matrix and the transformation it produces.
	www.ohiorc.org /ohiorc_resource_display.aspx?recId=4101 (156 words)

	TONC: The Affine Transformation Matrix
		The fl axes are the normal base vectors (note that y points down!), the blue axes are the transformed base vectors and the cyan variables are the arguments of the transformation.
		Well, traditionally R is given as that particular matrix, in which the angle runs from the x-axis towards the y-axis.
		The transformation matrix for this is A, which ties texel p to screen pixel q via q= A · p.
	user.chem.tue.nl /jakvijn/tonc/affine.htm (2162 words)

	Distributional Matrix Transformation Problem
		The distributional matrix transformation problem concerns with linear transformations on unimodular matrices.
		Linear transformations are chosen with respect to the uniform distribution on transformations of the same size.
		The distributional matrix transformation problem was shown to be average-case NP-complete by Gurevich [Gur90] and a full proof was published by Blass and Gurevich [BG95] using a randomized reduction.
	www.uncg.edu /mat/acc-forum/avgnp/node18.html (178 words)

	Problem with chaining transformation matrix-multiplication... - GameDev.Net Discussion Forums
		The thing is, my camera matrix is broken down into four matrices.
		The fourth matrix is the translation matrix which sets the camera's world position.
		When I first saw that I thought I was having some problems with the projection matrix but it wasn't that.
	www.gamedev.net /community/forums/viewreply.asp?ID=1858044 (944 words)

	how to change the transformation matrix? - HIT Lab NZ Forum
		We want to change the transformation matrix so that it is the same as we would
		We can get the transformation matrix for the first camera and for the second.
		I thought I could use the relation that the inverse of the first matrix multiplied by the second matrix gives the relation between marker2 and marker1,let´s say M3.
	www.hitlabnz.org /forum/showthread.php?p=282#post282 (237 words)

	Transformation Matrix Problem (Site not responding. Last check: 2007-11-03)
		This is problem 1.9 of Griffiths (3rd edition) text: Find the transformation matrix R that describes a rotation by 120 degrees about an axis from the origin through the point (1,1,1).
		The idea is that, since we use vectors to denote physical quantities and we want to manipulate the vectors with components relative to a coordinate system, it shouldn't matter how we choose such a coordinate system.
		The transformation matrix should tell you how to transform the components of the vector
	www.physicsforums.com /showthread.php?t=98138 (572 words)

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