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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).
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What is the definition of a Hermitian matrix?
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.
What is the dimension of hermitian matrix?
77
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 makes two matrices equal?
two matrices are normally considered equal only if they are identical. In other words, every element in the matrix must be equal to the corresponding element in the other matrix.
What is idempotent matrix?
An idempotent matrix is a matrix which gives the same matrix if we multiply with the same. in simple words,square of the matrix is equal to the same matrix. if M is our matrix,then MM=M. then M is a idempotent matrix.
What is the definition of a Hermitian matrix?
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.
What is the dimension of hermitian matrix?
77
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 harmitian matrix?
Hermitian matrix (please note spelling): a square matrix with complex elements that is equal to its conjugate transpose.
Why only complex numbers are used in unitary matrix?
It looks like that's part of the definition of a unitary matrix. See related link, below.
Why must the CKM matrix be unitary?
Unitary matrices leave the expectation value unchanged. We need the mixing matrix to be unitary (to preserve the mixed quarks as a basis, to preserve length); if VCKM were not unitary, it would perhaps suggest that a fourth generation of quarks needed to be considered or included.
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 density matrix in quantum mechanics?
In quantum mechanics, the density matrix is a mathematical representation of the state of a quantum system that is used to describe mixtures of quantum states or states that have uncertainty. It provides a way to calculate the average values of observables and predict the outcomes of measurements on the system.
What is the definition of unitary matrix?
It is the conjugate transpose of the matrix. Of course the conjugate parts only matters with complex entries. So here is a definition:A unitary matrix is a square matrix U whose entries are complex numbers and whose inverse is equal to its conjugate transpose U*. This means thatU*U = UU* = I. Where I is the identity matrix.
What is a Cabibbo-Kobayashi-Maskawa matrix?
A Cabibbo-Kobayashi-Maskawa matrix is a unitary matrix which specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions.
What is the possible determinant of unitary matrix?
|Det(U)| = 1 so that Det(U) = ±1
What is a Hermitian operator?
A Hermitian operator is a linear operator that is equal to its own adjoint. In other words, the adjoint of a Hermitian operator is the same as the operator itself. Hermitian operators play a key role in quantum mechanics as they correspond to observable physical quantities.
