CO OZNACZA SŁOWO NORMAL MATRIX
Matryca normalna
W matematyce złożona matryca kwadratowa A jest normalna, jeśli A * oznacza koniugat transpozycji A. Oznacza to, że matryca jest normalna, jeśli przemieszcza się ze swoim koniugatem transpozycji. Prawdziwa macierz A spełnia A * = AT, a więc jest normalna, jeśli ATA = AAT. Normalność jest wygodnym testem dla diagonalizacji: matryca jest normalna wtedy, gdy jest jednostkowo podobna do matrycy ukośnej, a zatem macierz A spełniająca równanie A * A = AA * jest przekątna. Koncepcja normalnych matryc może być rozszerzona na zwykłych operatorów na nieskończoną przestrzeń Hilberta i normalnych elementów w C * -algebrasie. Podobnie jak w przypadku matrycy, normalność oznacza zachowanie się komutacji w możliwie najszerszym zakresie w warunkach niekomercyjnych. To sprawia, że normalni operatorzy i zwykłe elementy C * -gebrasów, bardziej podatni na analizę.
Definicja słowa normal matrix w słowniku
Definicja normalnej macierzy w słowniku jest kwadratową macierzą A, dla której AA * = A * A, gdzie A * jest hermitowskim koniugatem A.
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1
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
2
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
* ...
3
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 ...
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
and ...
Roger A. Horn, Charles R. Johnson,
2012
5
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(
i2) ...
6
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.
153.
William J. Rea, Kalpana Patel,
2010
7
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∗
and ...
Sudipto Banerjee, Anindya Roy,
2014
8
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 ...
9
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 ...
10
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 ...
WIADOMOŚCI, KTÓRE ZAWIERAJĄ SŁOWO «NORMAL MATRIX»
Sprawdź, o czym dyskutuje się w prasie krajowej i zagranicznej oraz jak jest stosowane słowo
normal matrix w wiadomościach.
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, Lip 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, Maj 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, Sty 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, Gru 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, Kwi 14»
Trouble with accessing GLSL array
#version 130 uniform mat4 MVPMatrix; // combined model/view/projection matrix. uniform mat4 NMatrix; // normal matrix. uniform mat4 ... «Devmaster, Mar 14»
Normals in World Space from a GLSL Shader
The normal matrix is created via first transposing and then inverting the upper 3×3 part of the world (or world-view) matrix. normalMat ... «GameDev.net, Paz 13»
3D Biomatrix Publishes Application Notes with Novartis …
The model was analyzed via immunohistochemistry and was found to have a normal matrix distribution and proliferative zones. A preliminary ... «PR Web, Paz 13»