10 ENGLISH BOOKS RELATING TO «HERMITIAN MATRIX»
Discover the use of
Hermitian matrix in the following bibliographical selection. Books relating to
Hermitian matrix and brief extracts from same to provide context of its use in English literature.
1
Elements of Group Theory for Physicists
For this we note that if H is a hermitian matrix, exp(i/f ) is a unitary matrix. The
converse is also true, i.e., if U is any unitary matrix, then it can be expressed in
the form U = exp(itf), (4.94) where H is a hermitian matrix. Now any linear
combination ...
5-12] CONGRUENT AUTOMORPHS 103 APPENDIX 5-10 Rank of a Hermitian
matrix. The result presented in Theorem 4-11 shortens the work of determining
the rank of a matrix by means of subdeterminants. For Hermitian or symmetric ...
3
Problems and Theorems in Linear Algebra
Prove that if the rank of a symmetric (or Hermitian) matrix A is equal to r, then it
has a nonzero principal /..minor. 19.6. Let S be a symmetric invertible matrix of
order n all elements of which are positive. What is the largest possible number of
...
Viktor Vasilʹevich Prasolov, Simeon Ivanov, 1994
4
The Electrical Engineering Handbook,Second Edition
The concept of signal restoration can be used for this purpose if it is possible to
develop a closed-form expression for the operator that maps a general Hermitian
matrix into the closest positive-semidefinite Hermitian matrix in the Frobenius ...
Since a Hermitian matrix is normal (AA* : A2 : A*A), all the results about normal
matrices in Chapter 2 apply to Hermitian matrices. For example, eigenvectors
associated with distinct eigenvalues are orthogonal, there is an orthonormal
basis of ...
Roger A. Horn, Charles R. Johnson, 2012
6
Matrix theory and applications
A Hermitian matrix A is positive definite if x*Ax > 0 for all nonzero x e t"; A is
positive semide finite ifx*Ax>0 for all i e Cn; A is negative definite or semidefinite,
respectively, if -A is positive definite or semidefinite, respectively. A Hermitian
matrix ...
7
The Theory of Matrices: With Applications
In particular, A is Hermitian if A* = A. Thus, using Theorem 5.2.3, it is apparent
that a Hermitian matrix is normal and so they have all the properties of normal
matrices established in the previous section. Theorem 1. The spectrum of a
Hermitian ...
Peter Lancaster, Miron Tismenetsky, 1985
8
Matrices and Tensors in Physics
Show that any hermitian matrix of order two can be expressed uniquely as a
linear combination of the four matrices of Eq. (51). 14. (a) Show that the maximum
number of linearly independent hermitian matrices of order 3 is 9. (b) Construct a
...
9
Linear Algebra: Challenging Problems for Students
Chapter 4 Special Matrices Definitions and Facts Hermitian Matrix. An n-square
complex matrix A = (a,-J-) is said to be a Hermitian matrix if A* = A; that is, a,~j = Q
for all i and j. In case of real matrices, we say that A is real symmetric if A' = A. A ...
Thus, the four concepts of a Hermitian matrix, a unitary matrix, a skew-Hermitian
matrix, and a Hermitian form specialize in the real case to a symmetric matrix, an
orthogonal matrix, a skew-symmetric matrix, and a quadratic form. For example ...
Karim M. Abadir, Jan R. Magnus, 2005
