What is left regular representation?

What is left regular representation?

For a finite group G, the left regular representation λ (over a field K) is a linear representation on the K-vector space V freely generated by the elements of G, i. e. they can be identified with a basis of V. Given g ∈ G, λg is the linear map determined by its action on the basis by left translation by g, i.e.

Why do we use unitary representation?

In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ G. The general theory is well-developed in case G is a locally compact (Hausdorff) topological group and the representations are strongly continuous.

Is the regular representation faithful?

For G any algebraic group, then the regular representation is faithful. Moreover, it has finite-dimensional faithful sub-representations.

What is G invariant?

A subgroup S of a group G is said to be an “invariant” subgroup if. (2.5) for every S ∈ S and every X ∈ G. Invariant subgroups are sometimes called “normal subgroups” or “normal divisors”.

How do you show an operator is unitary?

We say U : V −→ V is unitary or a unitary operator if U∗ = U−1. A complex matrix A ∈ Mnn(C) is unitary if A∗ = A−1. A real matrix A ∈ Mnn(C) is orthogonal if AT = A−1.

What does faithful representation mean in accounting?

The new basic definition of faithful representation is the “correspondence or agreement between the accounting measures or descriptions in financial reports and the economic phenomena they purport to represent.” (

What is the faithful representation principle?

Faithful representation is the concept that financial statements be produced that accurately reflect the condition of a business. For example, if a company reports in its balance sheet that it had $1,200,000 of accounts receivable as of the end of June, then that amount should indeed have been present on that date.

What is a symmetric representation?

A geometric representation of L is a representation into the lattice of subspaces of a vector space over some skew field.

What is standard representation of element?

In the typical periodic table, each element is listed by its element symbol and atomic number. For example, “H” denotes hydrogen, “Li” denotes lithium, and so on. Most elements are represented by the first letter or first two letters of their English name, but there are some exceptions.

What is an invariant function?

An invariant function is a total function on S that takes the same value before and after execution of the loop body (whenever the loop condition holds).

What is an algebraic invariant?

A quantity such as a polynomial discriminant which remains unchanged under a given class of algebraic transformations. Such invariants were originally called hyperdeterminants by Cayley.

What is a linear representation?

A linear representation is a representation on a category of vector spaces or similar (Vect, Mod, etc.) This is the most common flavor of representations.

What is meant by unitary operators?

In functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product. Unitary operators are usually taken as operating on a Hilbert space, but the same notion serves to define the concept of isomorphism between Hilbert spaces.

What is unitary operation in quantum mechanics?

Unitary operators involve transformations of state vectors which preserve their scalar products, i.e. whereˆU =ˆA − ( ˆ A), ( ˆ A)≡(ψ| ˆ Aψ), etc. For time-independent operators,ˆA, obtain Ehrenfest Theorem, ∂t(ψ| ˆ A|ψ) = i h (ψ|[ˆH, ˆ A]|ψ).

What is the difference between fair presentation and faithful representation?

Simply put, fair presentation is the end result that is expected to be achieved by maintaining principle qualitative characteristics and the application of accounting standards. Faithful presentation is one of the qualitative factor that enhances one of the four principle qualitative characteristics i.e. reliability.

What are the three components of faithful representation?

There are three characteristics of faithful representation: 1. Completeness (adequate or full disclosure of all necessary information), 2. Neutrality (fairness and freedom from bias), and 3. Free from error (no inaccuracies and omissions).

What is standard representation of atom?

Standard nuclear notation shows the chemical symbol, the mass number and the atomic number of the isotope. Example: the isotopes of carbon. The element is determined by the atomic number 6.