Abstract algebra | Linear algebra

Normal element

In mathematics, an element x of a *-algebra is normal if it satisfies This definition stems from the definition of a normal linear operator in functional analysis, where a linear operator A from a Hilbert space into itself is called unitary if where the adjoint of A is A∗ and the domain of A is the same as that of A∗. See normal operator for a detailed discussion. If the Hilbert space is finite-dimensional and an orthonormal basis has been chosen, then the operator A is normal if and only if the matrix describing A with respect to this basis is a normal matrix. (Wikipedia).

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Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/ma

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Related pages

Hilbert space | Functional analysis | Normal operator | Mathematics | *-algebra | Orthonormal basis | Matrix (mathematics)