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Topic: Unitary matrix

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Diagonal matrix

Inverse matrix

Hermitian matrix

Normal matrix

Orthogonal matrix

List of linear algebra topics

Matrix (mathematics)

Symmetric matrix

Matrix decomposition

SU(3)

Conjugate transpose

Matrix inversion

Identity matrix

Eigenvalue

Hermitian conjugate

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	PlanetMath: unitary (Site not responding. Last check: 2007-11-07)
		On the other hand, the representing matrix of a unitary transformation relative to an orthonormal basis is, in fact, a unitary matrix.
		A simple example of a unitary matrix is the change of coordinates matrix between two orthonormal bases.
		Unitary spaces, transformations, and matrices are of fundamental importance in quantum mechanics.
	planetmath.org /encyclopedia/UnitaryTransformation.html (307 words)

	Encyclopedia: Unitary matrix (Site not responding. Last check: 2007-11-07)
		Unitary operators In linear algebra, an orthogonal matrix is a square matrix G whose transpose is its inverse, i.
		In mathematics, the unitary group of degree n over the field F (which is either the field R of real numbers or the field C of complex numbers) is the group of n by n unitary matrices with entries from F, with the group operation that of matrix multiplication.
		In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication.
	www.nationmaster.com /encyclopedia/Unitary-matrix (888 words)

	Learn more about List of matrices in the online encyclopedia. (Site not responding. Last check: 2007-11-07)
		Diagonal matrix - All entries not on the main diagonal (the diagonal from the upper left to the lower right corner) are zero.
		Unitary matrix - A matrix whose conjugate transpose is its inverse.
		Permutation matrix - Matrix representation of a permutation.
	www.onlineencyclopedia.org /l/li/list_of_matrices.html (294 words)

	Unitary matrix - Wikipedia, the free encyclopedia
		In mathematics, a unitary matrix is an n by n complex matrix U satisfying the condition
		It follows from the isometry property that all eigenvalues of a unitary matrix are complex numbers of absolute value 1 (i.e.
		A unitary matrix is called special if its determinant is 1.
	en.wikipedia.org /wiki/Unitary_matrix (208 words)

	Matrix Reference Manual: Special Matrices
		A 3#3 orthogonal matrix is either a rotation matrix or else a rotation matrix plus a reflection in the plane of the rotation according to whether it is proper or improper.
		A Rotation matrix is orthogonal with a determinant of +1.
		A signature matrix is a diagonal matrix whose diagonal entries are all +1 or -1.
	www.ee.ic.ac.uk /hp/staff/dmb/matrix/special.html (4201 words)

	Unitary matrix -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		A unitary matrix in which all entries are real is the same thing as an (Click link for more info and facts about orthogonal matrix) orthogonal matrix.
		It follows from the isometry property that all (Click link for more info and facts about eigenvalue) eigenvalues of a unitary matrix are complex numbers of (A numerical value regardless of its sign) absolute value 1 (i.e.
		All unitary matrices are (Something regarded as a normative example) normal, and the (Click link for more info and facts about spectral theorem) spectral theorem therefore applies to them.
	www.absoluteastronomy.com /encyclopedia/U/Un/Unitary_matrix.htm (418 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)

	Unitary matrix, valve and fan housing for energy recovery - Patent 4396406
		The matrix box may, for example, rest upon the roof top, be suspended from the ceiling, or alternatively rest upon the floor of the building.
		The matrix box 14 comprises an outer housing 30 which is substantially rectangular in horizontal cross-section and has two ports 32 and 34 which are diagonally opposed from one another and located in the uppermost part of two laterally opposed walls of housing 30.
		The uppermost edge 38 of the matrix box 14 terminates in a flange which matingly cooperates with a conjugate flange 40 on the lowermost edge of the transition fitting 16, thereby forming a substantially airtight seal.
	www.freepatentsonline.com /4396406.html (3862 words)

	MathGroup Archive (2000/01) - Re: Eigensystem applied to a unitary matrix crashes Mathematica 4.
		Unitary matrices are sometimes also called orthogonal matrices, and have the property that their inverse is equal to the transpose of the matrix.
		The eigenvalues of a unitary matrix is always ±1 or complex conjugate pairs of modulus one.
		Unitary matrices have several uses, and it is a bit of a catastrophe (at least for me) if Mathematica fails on extracting the correct eigenvectors.
	hilbert.math.hr /arhive/mathgroup/2000/01/0169.html (524 words)

	Quantum Computations and Unitary Matrix Decompositions
		Abstract: Data states within a quantum computer are mathematically modelled by vectors of complex numbers, and a given quantum computation acts on each data state by applying a fixed unitary matrix.
		Thus, matrix decompositions which factor a unitary matrix provide an automated procedure for dividing a quantum computation into multiple, hopefully simpler subcomputations.
		We continue to discuss the canonical decomposition of 4x4 unitaries developed in the physics literature, which allows for generically optimal logic circuits for two-qubit computations.
	math.nist.gov /mcsd/Seminars/2003/2003-09-23-bullock.html (159 words)

	Quantum computer (Site not responding. Last check: 2007-11-07)
		On each step of the algorithm, that vector is modified by multiplying it by a unitary matrix.
		The unitary operations are performed by shooting a short pulse of radiation at the container of molecules.
		Multiplication by a matrix is a linear operation.
	www.sciencedaily.com /encyclopedia/quantum_computer (2850 words)

	Unitary 2 by 2 matrix Information (Site not responding. Last check: 2007-11-07)
		Unitary 2 By 2 Matrix are great for when you're looking to get better at unitary 2 by 2 matrix for selfish purposes.
		A general unitary 2 × 2 matrix can always be obtained from a product of these transformations.
		Re: Number of independent elements of a unitary matrix [2.10.2] On 02 Oct 2002, troemjaezc wrote: >Thanks for the answers.
	matrix.2newinfo1.info /matrix-spybreak/unitary-2-by-2-matrix.html (276 words)

	Mathematical Programming Glossary - U (Site not responding. Last check: 2007-11-07)
		This arises in (linear) integer programming because it implies a basic solution to the LP relaxation is integer-valued (given integer-valued right-hand sides), thus obtaining a solution simply by a simplex method.
		An example of a totally unimodular matrix is the node-arc incidence matrix of a network, so basic solutions of network flows are integer-valued (given integer-valued supplies and demands).
		A nonsingular matrix whose Hermitian adjoint equals its inverse (same as orthogonal for real-valued matrices).
	www.cudenver.edu /~hgreenbe/glossary/U.html (481 words)

	Downdating of Szego polynomials
		In [5], the QR algorithm for unitary Hessenberg matrices is formulated in terms of the Schur parameters of the intermediate matrices.
		In [10], the approximation problem (1.6) is solved using the IUQR algorithm to construct the Schur parameters of the unitary Hessenberg matrix H.
		An efficient implementation is obtained by using the QR algorithm for unitary Hessenberg matrices described in [5].
	www.math.niu.edu /~ammar/downdate/node2.html (1438 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		SORMLQ Multiplies a general matrix by the orthogonal or unitary CUNMLQ matrix from an LQ factorization determined by SGELQF or CGELQF.
		SORMQL Multiplies a general matrix by the orthogonal or unitary CUNMQL matrix from a QL factorization determined by SGEQLF or CGEQLF.
		SORMQR Multiplies a general matrix by the orthogonal or unitary CUNMQR matrix from a QR factorization determined by SGEQRF or CGEQRF.
	www.sdsc.edu /SDSCwire/Services/c90_opt_08_27_97/lapack.txt (8350 words)

	[No title]
		JOBU (input) CHARACTER1 = 'U': U must contain a unitary* matrix U1 on entry, and the product U1U is returned; = 'I': U is initialized to the unit matrix, and the unitary* matrix U is returned; = 'N': U is not computed.
		JOBV (input) CHARACTER1 = 'V': V must contain a unitary* matrix V1 on entry, and the product V1V is returned; = 'I': V is initialized to the unit matrix, and the unitary* matrix V is returned; = 'N': V is not computed.
		JOBQ (input) CHARACTER1 = 'Q': Q must contain a unitary* matrix Q1 on entry, and the product Q1Q is returned; = 'I': Q is initialized to the unit matrix, and the unitary* matrix Q is returned; = 'N': Q is not computed.
	www.ibiblio.org /gferg/ldp/man/manl/ctgsja.l.html (678 words)

	Standard Groups
		Construct a matrix group over the field K (or over GF(q)) which has the adjoint Chevalley group of Lie series s and Lie rank n as the quotient modulo scalar matrices.
		Given a matrix group G over the finite field K and a subfield S of K, construct the semilinear extension of G over the subfield S.
		Given a matrix group G and a permutation group H, construct action of the wreath product on the tensor power of G by H, which is the (image of) the wreath product in its action on the tensor power (of the space that G acts on).
	www.math.wisc.edu /help/magma/text317.html (1638 words)

	Constructing a Unitary Hessenberg Matrix from Spectral Data - Ammar, Gragg, Reichel (ResearchIndex)
		Abstract: We consider the numerical construction of a unitary Hessenberg matrix from spectral data using an inverse QR algorithm.
		Any unitary upper Hessenberg matrix H with nonnegative subdiagonal elements can be represented by 2n \Gamma 1 real parameters.
		We show that a unitary upper Hessenberg matrix H with positive subdiagonal elements is determined...
	citeseer.ist.psu.edu /ammar91constructing.html (589 words)

	Physics at Minnesota:
		On exit, the upper triangle and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H, and the rest is set to zero.
		If COMPQ='I': on entry, Q need not be set, and on exit it contains the unitary matrix Q, where Q' is the product of the Givens transformations which are applied to A and B on the left.
		If COMPZ='I': on entry, Z need not be set, and on exit it contains the unitary matrix Z, which is the product of the Givens transformations which are applied to A and B on the right.
	www.physics.umn.edu /support/doc/cxml/zgghrd.3lapack.html?printer=yes (617 words)

	On the Digraph of a Unitary Matrix
		On the Digraph of a Unitary Matrix: SIAM Journal on Matrix Analysis and Applications Vol.
		Given a matrix M of size n, the digraph D on n vertices is said to be the digraph of M, when $M_{ij}\neq 0$ if and only if (v,sub>i,v,sub>j) is an arc of D.
		We observe that strong quadrangularity is sufficient to show that disconnected strongly regular graphs are the digraphs of unitary matrices and that n-paths, n-paths with loops at each vertex, n-cycles, directed trees, and trees are not.
	epubs.siam.org /sam-bin/dbq/article/41029 (187 words)

	Random matrices and the Riemann zeta function (Site not responding. Last check: 2007-11-07)
		Although an individual matrix with fixed entries cannot meaningfully be said to be 'random', it is possible to precisely define 'random matrix ensembles' in terms of probability distributions.
		Hughes, J. Keating, and N. O'Connell, "Random Matrix Theory and the Derivative of the Riemann Zeta Function", Proceedings of the Royal Society A456 (2000) 2611-2627.
		Hughes, "Central limit theorems and large deviations for the characteristic polynomial of a random unitary matrix and the Riemann zeta function" (a talk given at the DMV seminar "The Riemann zeta function and random matrix theory", Oct 2000)
	www.maths.ex.ac.uk /~mwatkins/zeta/random.htm (4483 words)

	On the Characteristic Polynomial of a Random Unitary Matrix (Site not responding. Last check: 2007-11-07)
		The analogy between the characteristic polynomial of a random unitary matrix and Riemann's zeta function was first studied by Keating and Snaith in \cite{KS1}.
		In particular, we present a range of fluctuation and large deviation results for the logarithm of the characteristic polynomial, as the matrix size tends to infinity.
		This naturally leads to the study discrete moments of the derivative of zeta, evaluated at the non-trivial zeros, whose asymptotics are then conjectured from a random matrix calculation.
	www.aimath.org /~hughes/PhD_abstract.html (272 words)

	unitary rotation matrix physics (Site not responding. Last check: 2007-11-07)
		Here is the in relation to unitary rotation matrix physics.
		Sometimes when you're trying to find submissions and support from ill-advised unitary rotation matrix physics excellent so it is imperative to know suggestions or help information relating to unitary rotation matrix physics, how to moderate the information you are presented with.
		Any reputable site providing information about unitary rotation matrix physics, about the webmaster's depth of experience, You can then decide for yourself will almost always provide an 'about' or 'contact' page about the vendor's education and practical knowledge, to advise people on the subject of unitary rotation matrix physics.
	www.pergola-news.info /physics/unitary-rotation-matrix-physics.htm (155 words)

	NAG Fortran Library Manual, Mark 21 : Keyword Index (unitary) (Site not responding. Last check: 2007-11-07)
		Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations
		Unitary reduction of complex general rectangular matrix to bidiagonal form
		Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
	www.nag.co.uk /numeric/fl/manual/html/indexes/kwic/fl_unitary.html (230 words)

	chseqr(l): compute eigenvalues of complex upper ... - Linux man page
		CHSEQR - compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T ZH, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix** of Schur vectors
		CHSEQR computes the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T ZH, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix** of Schur vectors.
		Optionally Z may be postmultiplied into an input unitary matrix Q, so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the unitary matrix Q: A = QHQ*H = (QZ)T(QZ)H. JOB (input) CHARACTER1
	www.die.net /doc/linux/man/manl/chseqr.l.html (513 words)

	Unitary matrix, valve and fan housing for energy recovery - Patent 4322229
		Unitary matrix, valve and fan housing for energy recovery - Patent 4322229
		The ventilation system according to claim 1 wherein said means connecting said third and fourth chambers to an outlet comprises a separate transition housing mounted to the other end of said matrix outer housing having passages therein in communication with said third and fourth channels.
		The ventilation system according to claim 2 wherein said means connecting said third and fourth channel to an outlet further includes a separate weather shield mounted to said transition housing and having outlets in communication with a respective one of said transition passages.
	www.freepatentsonline.com /4322229.html (3865 words)

	The Solution Space of the Unitary Matrix Model String Equation and the Sato Grassmannian - Anagnostopoulos, Bowick, ... (Site not responding. Last check: 2007-11-07)
		Abstract: The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined.
		It is shown that the string equation is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr.
		Unitary One Matrix Models: String Equation and Flows - Anagnostopoulos, Bowick (1991)
	citeseer.ist.psu.edu /473229.html (837 words)

	unitary matrix (Site not responding. Last check: 2007-11-07)
		i wanna know what unitary matrix is and what conditions have to be met so a matrix called unitary matrix
		A square matrix U is a unitary matrix if
		if a matrix's conjugate transpose is equal to its inverse, then the matrix is unitary matrix.
	www.edaboard.com /ftopic101724.html (45 words)

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