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	Woodbury matrix identity - Wikipedia, the free encyclopedia
		In mathematics (specifically linear algebra), the Woodbury matrix identity says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix.
		In the special case where C is the 1-by-1 unit matrix, reduces to the Sherman-Morrison formula.
		In case of the Kalman filter this matrix has the dimensions of the vector of observations, i.e., as small as 1 in case only one new observation is processed at a time.
	en.wikipedia.org /wiki/Woodbury_matrix_identity (303 words)

	Identity Matrix (Site not responding. Last check: 2007-11-07)
		The matrix I is called an identity matrix because IA = A and AI = A for all matrices A.
		There is no matrix that works as an identity for matrices of all dimensions.
		At left is an example of an identity matrix.
	chortle.ccsu.edu /VectorLessons/vmch16/vmch16_4.html (145 words)

	Matrix Algebra
		Elements (entries) of the matrix are referred to by the name of the matrix in lower case with a given row and column (again, row comes first).
		(The main or principal diagonal in matrix B is composed of elements all equal to 1.) With a square, symmetric matrix, the transpose of the matrix is the original matrix.
		Multiplying a matrix by the identity matrix is analogous to the real number operation of multiplying a number or variable by 1: the resulting output is identical to the numbers input.
	luna.cas.usf.edu /~mbrannic/files/regression/matalg.html (1775 words)

	Identity matrix - Wikipedia, the free encyclopedia
		represents the identity function, regardless of the basis.
		The unit vectors are also the eigenvectors of the identity matrix, all corresponding to the eigenvalue 1, which is therefore the only eigenvalue and has multiplicity n.
		It follows that the determinant of the identity matrix is 1 and the trace is n.
	en.wikipedia.org /wiki/Identity_matrix (222 words)

	identity matrix - Hutchinson encyclopedia article about identity matrix (Site not responding. Last check: 2007-11-07)
		Matrix which is the identity for multiplication in a family of matrices.
		is the unit matrix for 2 by 2 matrices.
		Identity Theft and Assumption Deterrence Act of 1998
	encyclopedia.farlex.com /identity+matrix (98 words)

	Matrix and Quaternion FAQ
		A matrix with M rows and N columns is defined as a MxN matrix.
		M where i=j ij In the case of the identity matrix, only the elements on the major diagonal are set to 1, while all others are set to 0.
		For all powers, the matrix must be square, that is orthogonal and the same width and height For example, -1 M is the inverse of the matrix 0 M generates the identity matrix 1 M leaves the matrix unchanged.
	www.j3d.org /matrix_faq/matrfaq_latest.html (7736 words)

	PlanetMath: identity matrix (Site not responding. Last check: 2007-11-07)
		, and the identity matrix is uniquely defined by this property.
		Cross-references: diagonal matrix, matrix exponential, eigenvectors, multiplicity, eigenvalue, trace, determinant, satisfy, property, standard matrix multiplication, matrices, multiplicative identity, identities, additive, multiplicative, represent, square matrix, ring
		This is version 8 of identity matrix, born on 2002-01-04, modified 2004-04-30.
	planetmath.org /encyclopedia/IdentityMatrix.html (107 words)

	SparkNotes: Matrices: The Identity Matrix
		The identity property of addition states that when zero is added to any real number, the number does not change.
		The identity property of multiplication states that when 1 is multiplied by any real number, the number does not change; that is, any number times 1 is equal to itself.
		When any m×n matrix is multiplied on the left by an m×m identity matrix, or on the right by an n×n identity matrix, the m×n matrix does not change.
	www.sparknotes.com /math/algebra2/matrices/section3.rhtml (193 words)

	Identity and Inverse Matrices
		The identity matrix I for multiplication is a square matrix with a 1 for every element of the principal diagonal (top left to bottom right) and a 0 in all other positions.
		Whenever the identity element for an operation is the answer to a problem, then the two items operated on to get that answer are inverses of each other.
		If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.
	www.blc.edu /fac/rbuelow/CAL/nt6-4.htm (209 words)

	Identity matrix
		In linear algebra, the identity matrix is a matrix which is the identity element under matrix multiplication.
		That is, multiplication of any matrix by the identity matrix (where defined) has no effect.
		, the identity matrix of size n is defined as a diagonal matrix with 1 in every entry of its main diagonal.
	www.brainyencyclopedia.com /encyclopedia/i/id/identity_matrix.html (185 words)

	Linear Algebra (Math 2318) - Systems of Equations and Matrices - Matrices (Site not responding. Last check: 2007-11-07)
		In this matrix the number of rows is equal to the number of columns. Matrices that have the same number of rows as columns are called square matrices.
		We don’t generally subscript the size of the matrix as we did in the second case, but on occasion it may be useful to make the size clear and in those cases we tend to subscript it as shown in the second case.
		As we’ll see identity matrices will arise fairly regularly. Here is a nice theorem about the reduced row-echelon form of a square matrix and how it relates to the identity matrix.
	tutorial.math.lamar.edu /AllBrowsers/2318/Matrices.asp (1623 words)

	Identity Design Matrix
		The matrix is filled with zeros, and ones on the main diagonal.
		This command is useful in filling the matrix after you have filled cells with incorrect values.
		After the matrix is filled with an identity matrix, it would look like this.
	www.warnercnr.colostate.edu /~gwhite/mark/markhelp/identity.htm (107 words)

	Matrix Simulation
		Since the red vector is the first row of the matrix, it is equal to the image of the (1,0) vector under the transformation described by the matrix.
		Since the matrix is a linear transformation, all the lines in the design will remain straight, and the Z will always be centered at the origin.
		If the matrix is set to the identity matrix (or a scalar multiple), then no eigenvectors are shown because there are no two unique eigenvectors; any vector is an eigenvector.
	www.falstad.com /matrix (967 words)

	Multiplication of Matrices
		Matrix multiplication changes dimensions; so it's hard to talk about a unit element in general.
		A fruitful approach is to confine the study to square (m=n) matrices of the same dimension.
		(In matrix theory, the matrix is known as the identity matrix.
	www.cut-the-knot.org /do_you_know/mul_mat.shtml (372 words)

	The Inverse of a Matrix
		An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.
		An elementary matrix is a matrix that is obtained by performing a single elementary row operation to an identity matrix.
		An elementary row operation is the process of either (1) replacing one row of a matrix with the sum of itself and a multiple of another row (2) Interchanging two rows (3) Multiplying all entries in a row by a nonzero constant.
	www.math.nyu.edu /~neylon/linalgfall04/project1/jja/group7.htm (1427 words)

	Matrix (GeoAPI 2.1 alpha) (Site not responding. Last check: 2007-11-07)
		The API for this interface matches closely the API in various matrix implementations available in Java3D, which should enable straightforward implementations.
		Java3D provides matrix for the general case and optimized versions for 3×3 and 4×4 cases, which are quite common in a transformation package.
		Retrieves the value at the specified row and column of this matrix.
	geoapi.sourceforge.net /snapshot/javadoc/org/opengis/referencing/operation/Matrix.html (160 words)

	The inverse of an nxn matrix
		Pivot on matrix elements in positions 1-1, 2-2, 3-3, continuing through n-n in that order, with the goal of creating a copy of the identity matrix
		Below is the same matrix A, augmented by the 3x3 identity matrix.
		The columns of the 3x3 identity matrix are colored blue as they re-appear on the left side
	math.uww.edu /faculty/mcfarlat/inverse.htm (441 words)

	Matrix Inversion
		Multiplying the inverse by the original matrix should give the identity matrix.
		Multiplying by the original matrix gives you an identity matrix with small numerical errors.
		can usually not tell for certain whether or not the matrix is singular: all it can tell is for example that the determinant is small compared to the entries of the matrix.
	documents.wolfram.com /v4/MainBook/3.7.6.html (296 words)

	Identity Matrix (DSP Blockset)
		Generate a matrix with ones on the main diagonal and zeros elsewhere.
		The Identity Matrix block generates a rectangular matrix with ones on the main diagonal and zeros elsewhere.
		When the Inherit output port attributes from input port check box is not selected, the input port is disabled, and the dimensions of the output matrix are determined by the Matrix size parameter.
	www.weizmann.ac.il /matlab/toolbox/dspblks/identitymatrix.html (565 words)

	6.2 - Operations with Matrices
		The number of columns in the first matrix must be equal to the number of rows in the second matrix.
		Since the number of columns in the first matrix is equal to the number of rows in the second matrix, you can pair up entries.
		Each element in row i from the first matrix is paired up with an element in column j from the second matrix.
	www.richland.edu /james/lecture/m116/matrices/operations.html (833 words)

	Matrix Operations, Part 3
		A square matrix with ones on the main diagonal and zeros everywhere else is called an identity matrix.
		A matrix of any size with all zero entries is called a zero matrix.
		A matrix with zeros everywhere except possibly on the main diagonal in called a diagonal matrix.
	www.math.duke.edu /education/ccp/materials/diffeq/matrix/matr3.html (256 words)

	Matrix and Quaternion FAQ (Site not responding. Last check: 2007-11-07)
		Also, the resulting matrix has an order of AxD Thus, it is possible to multiply a 4xN matrix with a 4x4 matrix but not the other way around.
		have the same width and height For example, -1 M is the inverse of the matrix 0 M generates the identity matrix 1 M leaves the matrix undamaged.
		Using a 4x4 matrix library, the algorithm is as follows: ---------------------------------------------------------------------- for (n = 0; n < 4; n++) m4_to_spherical(mat[n], andv_sph[n]); /* Spherical coordinates / m4_multspline(m_cardinal, v_sph, v_interp); / Interpolation vector */...
	www.flipcode.com /documents/matrfaq.html (7478 words)

	Summary: Matrix Algebra
		, of a matrix A is the matrix obtained from A by writing its rows as columns.
		In general, matrix multiplication is not commutative: AB is not equal to BA in general.
		If A is a square matrix, one that has the same number of rows and columns, it is sometimes possible to take a matrix equation such as AX = B and solve for X by "dividing by A." Precisely, a square matrix A may have an
	www.zweigmedia.com /ThirdEdSite/Summary3.html (611 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Use elementary row operations to transform the matrix on the left side of the vertical line to the 3 x 3 identity matrix.
		When the matrix on the left is transformed to the 3 x 3 identity matrix, the matrix on the right of the vertical line is the inverse.
		Property of the identity matrix (I is the n x n identity matrix since X is n x p).
	www.nccu.edu /artsci/math/melikyan/mat_fm/lec/lec4_5.ppt (1239 words)

	[No title]
		Determinants are useful in finding the inverse of a matrix, that is, the matrix that when multiplied by A yields the identity matrix.
		When defining a matrix, one puts brackets about the data points and commas at the end of each row of the matrix.
		The last matrix is, within rounding error, an identity matrix, obtained by multiplying the variance-covariance matrix by its inverse.
	core.ecu.edu /psyc/wuenschk/MV/MultReg/Invert.doc (397 words)

	Matrix Multiplication Lesson - II
		Because the identity matrix you need will depend upon the size of the matrix that it is being multiplied on!
		on the left by the identity, you have to use
		in the above example), the identity matrix you use will depend upon the side that you're multiplying on.
	www.purplemath.com /modules/mtrxmult2.htm (324 words)

	GameDev.net - 3D Matrix Math Demystified (Site not responding. Last check: 2007-11-07)
		The Identity Matrix, which produces no rotation at all, simply has an X Axis Vector of (1, 0, 0), a Y Axis Vector of (0, 1, 0), and a Z Axis Vector of (0, 0, 1).
		Usually you also want to have a matrix be able to translate, or shift, a point through space as well as rotate it, and that sort of operation is called an "Affine" transformation.
		If the matrix was representing a jet plane's orientation in the world, the Translation Vector would merely be the coordinates of the center of the jet plane in the world.
	www.gamedev.net /reference/articles/article695.asp (2045 words)

	MSN Encarta - Dictionary - identity matrix definition
		MSN Encarta - Dictionary - identity matrix definition
		Search for "identity matrix" in all of MSN Encarta
		matrix with 1 on main diagonal: a square matrix that has the numeral 1 in each position on the principal diagonal and 0 in all other positions
	encarta.msn.com /encnet/features/dictionary/DictionaryResults.aspx?refid=1861695015 (82 words)

	SparkNotes: Matrices: Introduction and Summary
		The second section explains two types of multiplication associated with matrices: scalar multiplication--that is, multiplication by a constant--and multiplication of two matrices.
		Just as there is an additive identity and a multiplicative identity for all real numbers (an addition and a multiplication that does not change the number), there is an additive identity and a multiplicative identity for all matrices.
		Just as most real numbers have a multiplicative inverse, most matrices also have multiplicative inverse--that is, a matrix that, when multiplied by the original matrix, yields the identity.
	www.sparknotes.com /math/algebra2/matrices/summary.html (379 words)

	Matrix Multiplication
		Thus, the number of columns in the matrix on the left must equal the number of rows in the matrix on the right.
		filtering operation can be expressed as a matrix multiply applied to the input signal.
		LTI) filtering operation can be expressed as a matrix multiply in which the matrix is Toeplitz, i.e.
	ccrma-www.stanford.edu /~jos/mdft/Matrix_Multiplication.html (232 words)

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