Algor mortis

I'm Fernando (21) from Seltjarnarnes, Iceland.
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my site; wellness [continue reading this..] In mathematics, a unitary transformation may be informally defined as a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.

More precisely, a unitary transformation is an isomorphism between two Hilbert spaces. In other words, a unitary transformation is a bijective function

$U:H_1\to H_2$

where $H_1$ and $H_2$ are Hilbert spaces, such that

$⟨Ux,Uy⟩=⟨x,y⟩$

for all $x$ and $y$ in $H_1$. A unitary transformation is an isometry, as one can see by setting $x=y$ in this formula.

In the case when $H_1$ and $H_2$ are the same space, a unitary transformation is an automorphism of that Hilbert space, and then it is also called a unitary operator.

A closely related notion is that of antiunitary transformation, which is a bijective function

$U:H_1\to H_2$

between two complex Hilbert spaces such that

$⟨Ux,Uy⟩=\overline{⟨x,y⟩}=⟨y,x⟩$

for all $x$ and $y$ in $H_1$, where the horizontal bar represents the complex conjugate.

See also

• Antiunitary
• Orthogonal transformation
• Time reversal
• Unitary group
• Unitary operator
• Unitary matrix
• Wigner's Theorem