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).
Matrices are tools to solve linear equations. Engineers use matrices in solving electrical problems in circuits using Thevenin's and Norton's theories.
Please clarify what you want to "solve". There are several operations you can do with matrices, such as add them, multiply them, transpose them, etc.
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.
Matrices are generally used to solve simultaneous equations. You use the co-efficient of the variables and arrange them in a matrix to solve them. To do so requires at least as many equation as there are variables. Other uses include vector calculations.
The question contains expressions, not equations. It is not possible to solve linear expressions - whether you use matrices or not.
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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.
The most common use for inverted matrices is to solve a set of simultaneous equations.
No. Determinants are only defined for square matrices.No. Determinants are only defined for square matrices.
A Hermitian operator is any linear operator for which the following equality property holds: integral from minus infinity to infinity of (f(x)* A^g(x))dx=integral from minus infinity to infinity of (g(x)A*^f(x)*)dx, where A^ is the hermitian operator, * denotes the complex conjugate, and f(x) and g(x) are functions. The eigenvalues of hermitian operators are real and their eigenfunctions are orthonormal.
It isn't clear what you want to solve for. If you want to find the matrix, there is not a unique solution - there are infinitely many matrices with the same determinant.