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WHAT DOES NORMAL MATRIX MEAN IN ENGLISH?
In mathematics, a complex square matrix A is normal if where A∗ is the conjugate transpose of A. That is, a matrix is normal if it commutes with its conjugate transpose. A real matrix A satisfies A∗ = AT, and is therefore normal if ATA = AAT. Normality is a convenient test for diagonalizability: a matrix is normal if and only if it is unitarily similar to a diagonal matrix, and therefore any matrix A satisfying the equation A∗A = AA∗ is diagonalizable. The concept of normal matrices can be extended to normal operators on infinite dimensional Hilbert spaces and to normal elements in C*-algebras. As in the matrix case, normality means commutativity is preserved, to the extent possible, in the noncommutative setting. This makes normal operators, and normal elements of C*-algebras, more amenable to analysis.
Synonyms and antonyms of normal matrix in the English dictionary of synonyms
WORDS RELATING TO «NORMAL MATRIX»
The translations of normal matrix from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «normal matrix» in English.
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «normal matrix».
FREQUENCY OF USE OF THE TERM «NORMAL MATRIX» OVER TIME
The graph expresses the annual evolution of the frequency of use of the word «normal matrix» during the past 500 years. Its implementation is based on analysing how often the term «normal matrix» appears in digitalised printed sources in English between the year 1500 and the present day.
Examples of use in the English literature, quotes and news about normal matrix
10 ENGLISH BOOKS RELATING TO «NORMAL MATRIX»
Discover the use of normal matrix in the following bibliographical selection. Books relating to normal matrix and brief extracts from same to provide context of its use in English literature.
Matrix Variate Distributions
Matrix Variate Distributions gathers and systematically presents most of the recent developments in continuous matrix variate distribution theory and includes new results.
A K Gupta, D K Nagar, 1999
Encyclopedic Dictionary of Mathematics
If A A* = A*A, then A is said to be a normal matrix. A matrix U such that U*U = /,
that is, U'1 = U*, is normal. Following G. Frobenius, we call it a unitary matrix (in
the following discussion, we shall call it simply a u-matrix). A matrix H such that H
Kiyosi Itô, 1993
Elementary Matrix Theory
IT a\ 5.9-6 Prove that every normal matrix with real characteristic roots is
Hermitian. 5.9-7 Show that a normal matrix is similar to its transpose. 5.9-8 Prove
that two normal matrices are unitarily similar if and only if they are similar. 5.9-9 If
C is a ...
Howard Eves, 2012
P2 Show that a normal matrix is unitary if and only if all its eigenvalues have
absolute value 1. 2.5.P3 Show that a normal matrix is Hermitian if and only if all
its eigenvalues are real. 2.5.P4 Show that a normal matrix is skew Hermitian if
Roger A. Horn, Charles R. Johnson, 2012
Mechatronic Systems 2004
The normal matrix can be identified in (3.1) as If the normal matrix is 'near
singular' then the solution for the least-squares method becomes ill-conditioned.
The condition number of the normal matrix is defined as «(R) = (14) where Amoa(
Reza Moheimani, 2005
Reversibility of Chronic Degenerative Disease and ...
Heine H and Anastasiadis P. 1992. Normal Matrix and Pathological Conditions.
New York: Gustar Fischer Verlag. 77. 75. Heine H and Anastasiadis P. 1992.
Normal Matrix and Pathological Conditions. New York: Gustar Fischer Verlag.
William J. Rea, Kalpana Patel, 2010
Linear Algebra and Matrix Analysis for Statistics
To prove the “if” part, we assume that A is an n × n normal matrix. By the Schur's
Triangularization Theorem, there exists a unitary matrix P and an upper-
triangular matrix T such that A = PTP∗. Note that AA∗ = PTP∗PT∗P∗ = PTT∗P∗
Sudipto Banerjee, Anindya Roy, 2014
Matrix Theory: Basic Results and Techniques
Let A I (atj) be a normal matrix. If K is a It >< It principal submatrix of A, we denote
by E(K) the sum of all entries of K . Show that h|A| Z maxK |E(K)| for at least one
eigenvalue A of A. Let A I (atj) be an n-square complex matrix and denote mi I ...
Fuzhen Zhang, 2011
The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods
A second confirmation of this fact comes from the realization that the left
eigenvectors of a normal matrix are essentially the same as the right
eigenvectors (Exercise 2.7.18). Specifically, if v is a right eigenvector, then it" is
an associated left ...
David S. Watkins, 2007
Beginning OpenGL Game Programming
The Normal Matrix All of the lighting calculations are performed in eye space. As
we covered in Chapter 4, we use the modelview matrix to transform a vertex from
object space to eye space. Unfortunately, things aren't so simple when it comes ...
Jason Darby, 2009
10 NEWS ITEMS WHICH INCLUDE THE TERM «NORMAL MATRIX»
Find out what the national and international press are talking about and how the term normal matrix is used in the context of the following news items.
Voxel8 raises $12M to launch their electronics 3D printer by end of …
... designers and engineers of all skill levels to print embedded conductors, wires, and batteries into the normal matrix materials of 3D printing. «3ders.org, Jul 15»
Identification of novel drugs to target dormant micrometastases
MTD: Maximum tolerated dose. SIS: Small intestine submucosa. SISgel: A gel-forming normal matrix material prepared from SIS ... «BMC Blogs Network, May 15»
Normal mapping on flat water surface produces incorrect specular …
The transpose of the inverse of the upperleft 3x3 matrix of the model matrix gives a so called Normal Matrix that is a version of the model matrix ... «GameDev.net, Mar 15»
In-Q-Tel, CIA's venture-capital arm, invests in 3D electronics printing …
The company enables designers and engineers to print embedded conductors, wires, and batteries into the normal matrix materials of 3D ... «3ders.org, Mar 15»
Facebook, Apple, And Microsoft Are Ganging Up On Google
Seeking Opportunties @ Normal Matrix Organizations. I don't agree that Microsoft was an evil empire. From the tech giants of today , it was IBM ... «Pulse, Jan 15»
Get View Matrix from Model Matrix
This doesn't work, and I can understand why: the normal matrix is the inverse-transpose of the upper-left 3x3 section of the final model matrix. «GameDev.net, Dec 14»
4 Things You Can Fix About Your Aging Body
That's basically a synthetic version of the normal matrix that sits in the knee joint and prevents bone from rubbing on bone. Another option is an ... «Huffington Post, Apr 14»