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Hermitian matrix defined:
If a square matrix, A, is equal to its conjugate transpose, A†, then A is a Hermitian matrix.
Notes:
1. The main diagonal elements of a Hermitian matrix must be real.
2. The cross elements of a Hermitian matrix are complex numbers having equal real part values, and equal-in-magnitude-but-opposite-in-sign imaginary parts.
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What is the definition of a skew-Hermitian matrix?
Skew-Hermitian matrix defined:If the conjugate transpose, A†, of a square matrix, A, is equal to its negative, -A, then A is a skew-Hermitian matrix.Notes:1. The main diagonal elements of a skew-Hermitian matrix must be purely imaginary, including zero.2. The cross elements of a skew-Hermitian matrix are complex numbers having equal imaginary part values, and equal-in-magnitude-but-opposite-in-sign real parts.
What is the dimension of hermitian matrix?
77
Is every unitary matrix hermitian?
Absolutely not. They are rather quite different: hermitian matrices usually change the norm of vector while unitary ones do not (you can convince yourself by taking the spectral decomposition: eigenvalues of unitary operators are phase factors while an hermitian matrix has real numbers as eigenvalues so they modify the norm of vectors). So unitary matrices are good "maps" whiule hermitian ones are not. If you think about it a little bit you will be able to demonstrate the following: for every Hilbert space except C^2 a unitary matrix cannot be hermitian and vice versa. For the particular case H=C^2 this is not true (e.g. Pauli matrices are hermitian and unitary).
What is the definition of an idempotent matrix?
A square matrix A is idempotent if A^2 = A. It's really simple
Is the row space of matrix an equivalent to the column space of matrix AT which is the transpose of matrix A?
Since the columns of AT equal the rows of A by definition, they also span the same space, so yes, they are equivalent.
What is the definition of a skew-Hermitian matrix?
Skew-Hermitian matrix defined:If the conjugate transpose, A†, of a square matrix, A, is equal to its negative, -A, then A is a skew-Hermitian matrix.Notes:1. The main diagonal elements of a skew-Hermitian matrix must be purely imaginary, including zero.2. The cross elements of a skew-Hermitian matrix are complex numbers having equal imaginary part values, and equal-in-magnitude-but-opposite-in-sign real parts.
What is the dimension of hermitian matrix?
77
What is harmitian matrix?
Hermitian matrix (please note spelling): a square matrix with complex elements that is equal to its conjugate transpose.
What is density matrix in quantum mechanics?
It is a Hermitian positive-semidefinite matrix of trace one that describes the statistical state of a quantum system. Hermitian matrix is defined as A=A^(dagger). Meaning that NxN matrix A is equal to it's transposed complex conjugate. Trace is defined as adding all the terms on the diagonal.
Is every unitary matrix hermitian?
Absolutely not. They are rather quite different: hermitian matrices usually change the norm of vector while unitary ones do not (you can convince yourself by taking the spectral decomposition: eigenvalues of unitary operators are phase factors while an hermitian matrix has real numbers as eigenvalues so they modify the norm of vectors). So unitary matrices are good "maps" whiule hermitian ones are not. If you think about it a little bit you will be able to demonstrate the following: for every Hilbert space except C^2 a unitary matrix cannot be hermitian and vice versa. For the particular case H=C^2 this is not true (e.g. Pauli matrices are hermitian and unitary).
Can a Hermitian Matrix possess Complex Eigenvectors?
Yes. Simple example: a=(1 i) (-i 1) The eigenvalues of the Hermitean matrix a are 0 and 2 and the corresponding eigenvectors are (i -1) and (i 1). A Hermitean matrix always has real eigenvalues, but it can have complex eigenvectors.
What is the definition of involtary matrix?
Involtary Matrix A square matrix A such that A2=I or (A+I)(A-I)=0, A is called involtary matrix.
What is the definition of a null matrix?
The null matrix is also called the zero matrix. It is a matrix with 0 in all its entries.
What is payroll matrix?
can anyone give me an exact definition of payroll matrix................
What is the definition of zero matrix?
Zero Matrix When all elements of a matrix are zero than the matrix is called zero matrix. Example: A=|0 0 0|
What is the definition of identity matrix?
Identity or Unit Matrix If in the scaler matrix the value of k=1, the matrix is called the identity or unit matrix. It is denoted by I or U.
Definition of Lower-triangular matrix?
Lower-triangular Matrix A square matrix A whose elements aij=0 for i
