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How do you use Hermitian in a sentence? See 10+ example sentences showing how this word appears in different contexts, plus the exact meaning.

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Hermitian in a sentence

Hermitian meaning

Equal to its own transpose conjugate.

Using Hermitian

  • The main meaning on this page is: Equal to its own transpose conjugate.
  • In the example corpus, hermitian often appears in combinations such as: hermitian matrix, called hermitian, hermitian form.

Context around Hermitian

  • Average sentence length in these examples: 21.1 words
  • Position in the sentence: 6 start, 6 middle, 4 end
  • Sentence types: 16 statements, 0 questions, 0 exclamations

Often before:

non 1× maximally 1× necessarily 1× definite 1×

Often after:

matrix 4× form 2× products 2× symmetry 1× product 1× systems 1× operators 1× precisely 1× vector 1×

Sentence patterns with Hermitian

These short patterns come directly from the example sentences and show how the word is often embedded:

a hermitian matrix is 2× a maximally hermitian precisely by 1× also called hermitian symmetry and 1× and have hermitian products that 1× b are hermitian therefore z 1× called a hermitian form 1× defined by hermitian operators that 1× hermitian product spaces 1×

Sentence openings and endings

Common sentence openings:

a hermitian matrix 2× conjugate symmetry is 1× each observable is 1× hermitian product spaces 1× hermitian vector spaces 1× in summary the 1×

Common sentence endings:

a hermitian form 1× are individually real 1× argument by convention 1× be positive definite 1× definite hermitian form 1× eigenvalues are positive 1×

Words around Hermitian

Just before it in the word index:

hermite 15 hermitage 72 hermit 117 hermiston 18 hermione 137 herminie 3

Just after it in the word index:

hermitism 2 hermits 20 hermocrates 4 hermogenianus 2 hermon 36 hermond 2

Similar in corpus frequency:

aaaa 21 abductees 21 abdulahi 21 abetment 21 abhors 21 abidal 21

Corpus analysis for Hermitian

  • In this selection, "hermitian" usually appears near the start of the sentence. The average example has 21.1 words, and this corpus slice is mostly made up of statements.
  • Around the word, non, maximally, necessarily, matrix, form and products stand out and add context to how "hermitian" is used.
  • Recognizable usage signals include a hermitian matrix is and a maximally hermitian precisely by. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "hermitian" sits close to words such as aaaa, abductees and abdulahi, which helps place it inside the broader word index.

Example types with hermitian

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

It will be recalled that P is Hermitian. (8 words)

A Hermitian matrix is positive definite if all its eigenvalues are positive. (12 words)

Unlike Inner Products, Scalar Products and Hermitian Products need not be positive-definite. (13 words)

Longer example sentences

Hermitian vector spaces and spinors If the vector space V has extra structure that provides a decomposition of its complexification into two maximal isotropic subspaces, then the definition of spinors (by either method) becomes natural. (35 words)

Negative-definite, semidefinite and indefinite matrices A Hermitian matrix is negative-definite, negative-semidefinite, or positive-semidefinite if and only if all of its eigenvalues are negative, non-positive, or non-negative, respectively. (33 words)

But in this work, the team used a method that made these open systems accessible, and “we found interesting topological properties in these non-Hermitian systems,” Zhou says. (28 words)

Example sentences (16)

Conjugate symmetry is also called Hermitian symmetry, and a conjugate symmetric sesquilinear form is called a Hermitian form.

Hermitian Product Spaces are restricted to the field of complex numbers and have "hermitian products" that are conjugate-symmetrical and linear in the first argument(by convention).

But in this work, the team used a method that made these open systems accessible, and “we found interesting topological properties in these non-Hermitian systems,” Zhou says.

According to the postulates of quantum mechanics, such quantities are defined by Hermitian operators that act on the Hilbert space of possible states of a system.

A Hermitian matrix is positive definite if all its eigenvalues are positive.

A Hermitian matrix is positive semidefinite if and only if all of its principal minors are nonnegative.

Each observable is represented by a maximally Hermitian (precisely: by a self-adjoint ) linear operator acting on the state space.

Hermitian vector spaces and spinors If the vector space V has extra structure that provides a decomposition of its complexification into two maximal isotropic subspaces, then the definition of spinors (by either method) becomes natural.

Advertentie

Indefinite A Hermitian matrix which is neither positive definite, negative definite, positive-semidefinite, nor negative-semidefinite is called indefinite.

In summary, the distinguishing feature between the real and complex case is that, a bounded positive operator on a complex Hilbert space is necessarily Hermitian, or self adjoint.

It will be recalled that P is Hermitian.

Negative-definite, semidefinite and indefinite matrices A Hermitian matrix is negative-definite, negative-semidefinite, or positive-semidefinite if and only if all of its eigenvalues are negative, non-positive, or non-negative, respectively.

The matrices A and B are Hermitian, therefore z*Az and z*Bz are individually real.

This condition implies that M is Hermitian, that is, its transpose is equal to its conjugate.

Unlike Inner Products, Scalar Products and Hermitian Products need not be positive-definite.

While the above axioms are more mathematically economical, a compact verbal definition of an inner product is a positive-definite Hermitian form.

Advertentie

Common combinations with hermitian

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "hermitian" in a sentence?
An example: "Conjugate symmetry is also called Hermitian symmetry, and a conjugate symmetric sesquilinear form is called a Hermitian form." This page contains 10+ example sentences with the word "hermitian" from authentic English texts.
What does "hermitian" mean?
Hermitian means: Equal to its own transpose conjugate.
How many example sentences with "hermitian" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "hermitian", drawn from a database of millions of English sentences.