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Orthonormal is an English word. Below you'll find 10+ example sentences showing how it's used in practice.

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Orthonormal in a sentence

Orthonormal meaning

  1. Of a set of vectors, both orthogonal and normalized.
  2. Of a linear transformation: that preserves both angles and lengths.

Using Orthonormal

  • The main meaning on this page is: Of a set of vectors, both orthogonal and normalized. | Of a linear transformation: that preserves both angles and lengths.
  • In the example corpus, orthonormal often appears in combinations such as: orthonormal basis, an orthonormal, complete orthonormal.

Context around Orthonormal

  • Average sentence length in these examples: 22.9 words
  • Position in the sentence: 5 start, 6 middle, 6 end
  • Sentence types: 17 statements, 0 questions, 0 exclamations

Often before:

complete 2× containing 1×

Often after:

basis 11× sequence 1× systems 1× system 1× vectors 1× set 1×

Sentence patterns with Orthonormal

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

has an orthonormal basis 2× a complete orthonormal system of 1× an orthonormal basis is 1× an orthonormal sequence in 1× basis is orthonormal if if 1× complete orthonormal systems of 1× definition of orthonormal basis generalizes 1× form an orthonormal basis linear 1×

Sentence openings and endings

Common sentence openings:

an orthonormal basis 1× an orthonormal sequence 1× any complete inner 1× complete orthonormal systems 1× for simplicity we 1× in most cases 1×

Common sentence endings:

an orthonormal basis 5× 2 inner product 1× as illustrated above 1× called the eigenvalues 1× independent of time 1× parameterized by angle 1×

Words around Orthonormal

Just before it in the word index:

orthomolecular 2 orthography 148 orthographies 30 orthographically 4 orthographical 2 orthographic 37

Just after it in the word index:

orthopaedic 58 orthopaedics 21 orthopediatrics 3 orthopedic 110 orthopedics 29 orthopedist 5

Similar in corpus frequency:

aaaa 21 abductees 21 abdulahi 21 abetment 21 abhors 21 ablution 21

Corpus analysis for Orthonormal

  • In this selection, "orthonormal" usually appears in the middle of the sentence. The average example has 22.9 words, and this corpus slice is mostly made up of statements.
  • Around the word, complete, containing, basis, sequence and systems stand out and add context to how "orthonormal" is used.
  • Recognizable usage signals include has an orthonormal basis and a complete orthonormal system of. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "orthonormal" sits close to words such as aaaa, abductees and abdulahi, which helps place it inside the broader word index.

Example types with orthonormal

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

Any complete inner product space V has an orthonormal basis. (10 words)

The only possible measurement is between any two orthogonal states (an orthonormal basis). (13 words)

This is equivalent to the assertion that every Hilbert space has an orthonormal basis. (14 words)

Longer example sentences

This space is actually a Hilbert space with an inner product given for any two elements f and g by : The basic Fourier series result for Hilbert spaces can be written as : Sines and cosines form an orthonormal set, as illustrated above. (42 words)

In symbols, a basis is orthonormal if if and for each i. This definition of orthonormal basis generalizes to the case of infinite-dimensional inner product spaces in the following way. (31 words)

Complete orthonormal systems of wave functions appear naturally as the eigenfunctions of the Hamiltonian (of a bound system ) in quantum mechanics that measures the energy levels, which are called the eigenvalues. (31 words)

Example sentences (17)

In symbols, a basis is orthonormal if if and for each i. This definition of orthonormal basis generalizes to the case of infinite-dimensional inner product spaces in the following way.

An orthonormal basis is a basis where all basis vectors have length 1 and are orthogonal to each other.

An orthonormal sequence in a Hilbert space is a simple example of a weakly convergent sequence, with limit equal to the 0 vector.

Any complete inner product space V has an orthonormal basis.

Complete orthonormal systems of wave functions appear naturally as the eigenfunctions of the Hamiltonian (of a bound system ) in quantum mechanics that measures the energy levels, which are called the eigenvalues.

For simplicity, we assume that they are discrete, and that they are orthonormal, i.e., : Note that these basis states are assumed to be independent of time.

In most cases of practical interest, the orthonormal basis comes from an integral or differential operator, in which case the series converges in the distribution sense.

In other words, the Hermite functions form a complete orthonormal system of eigenfunctions for the Fourier transform on L 2 (R).

Advertentie

Spinors main When changing from one orthonormal basis (called a frame) to another by a rotation, the components of a tensor transform by that same rotation.

Suppose a circular path in an arbitrary plane containing orthonormal vectors and is parameterized by angle.

Then the sequence (indexed on set of all integers) of continuous functions : is an orthonormal basis of the space with the L 2 inner product.

The only possible measurement is between any two orthogonal states (an orthonormal basis).

These four pure states are all maximally entangled (according to the entropy of entanglement ) and form an orthonormal basis (linear algebra) of the Hilbert space of the two qubits.

The two previous theorems raise the question of whether all inner product spaces have an orthonormal basis.

This is equivalent to the assertion that every Hilbert space has an orthonormal basis.

This space is actually a Hilbert space with an inner product given for any two elements f and g by : The basic Fourier series result for Hilbert spaces can be written as : Sines and cosines form an orthonormal set, as illustrated above.

Using the Gram–Schmidt process we may start with an arbitrary basis and transform it into an orthonormal basis.

Advertentie

Common combinations with orthonormal

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "orthonormal" in a sentence?
An example: "In symbols, a basis is orthonormal if if and for each i. This definition of orthonormal basis generalizes to the case of infinite-dimensional inner product spaces in the following way." This page contains 10+ example sentences with the word "orthonormal" from authentic English texts.
What does "orthonormal" mean?
Orthonormal means: Of a set of vectors, both orthogonal and normalized.
How many example sentences with "orthonormal" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "orthonormal", drawn from a database of millions of English sentences.