HERMITIAN Meaning and
Definition
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Hermitian is an adjective used in mathematics and physics to describe a specific property of a matrix, operator, or function specifically related to linear algebra and quantum mechanics.
In linear algebra, a matrix or operator is said to be Hermitian if it is equal to its own conjugate transpose. This means that the matrix or operator is symmetric with respect to the complex conjugate. In simpler terms, a Hermitian matrix is one where the elements remain unchanged when complex conjugated and transposed.
In quantum mechanics, Hermitian operators play a crucial role in the mathematical description of physical observables. These operators represent physical properties, such as energy or momentum, and are associated with self-adjointness, which ensures real eigenvalues and orthogonal eigenvectors. When an operator in quantum mechanics is Hermitian, it guarantees that the corresponding physical observable will produce real-valued results when measured.
The term "Hermitian" is derived from the name of the French mathematician Charles Hermite, who made significant contributions to the theory of complex numbers and mathematical analysis. The Hermitian property has numerous applications in mathematics, physics, and engineering, particularly in areas such as quantum mechanics, signal processing, and optimization.
Common Misspellings for HERMITIAN
Etymology of HERMITIAN
The word "Hermitian" comes from the name "Hermite", derived from the Latin term "eremita", meaning "hermit". It is named after the French mathematician Charles Hermite, who made significant contributions to the field of mathematics, including the study of complex numbers and matrices. The term "Hermitian" is specifically associated with matrices and operators that satisfy a particular condition, which was formulated by Hermite and later refined by others. These matrices are called "Hermitian" in his honor.
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