- #1
wasi-uz-zaman
- 89
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hi, i know unitary transformation - but could not get where do we need finite and infinite unitary transformation ?
please help me in this regard.
thanks
please help me in this regard.
thanks
It is not that "we need" or don't need, rather it is the nature of the symmetry group that decides for us. For example, non-compact groups such as the Lorentz group does not have finite-dimensional unitary representations.wasi-uz-zaman said:hi, i know unitary transformation - but could not get where do we need finite and infinite unitary transformation ?
please help me in this regard.
thanks
A finite unitary transformation is a type of mathematical operation that preserves the inner product of a vector space. This means that the length and angles between vectors are maintained after the transformation is applied.
An infinite unitary transformation is a type of mathematical operation that preserves the inner product of an infinite-dimensional vector space. This means that the length and angles between vectors are maintained even when the number of dimensions is infinite.
The main difference between a finite and an infinite unitary transformation is the number of dimensions in the vector space they act upon. Finite unitary transformations are applied to finite-dimensional vector spaces, while infinite unitary transformations are applied to infinite-dimensional vector spaces.
Finite and infinite unitary transformations have various applications in physics, engineering, and computer science. They are used to model physical phenomena, analyze data, and optimize algorithms. For example, quantum mechanics uses infinite unitary transformations to describe the behavior of particles in an infinite-dimensional Hilbert space.
Finite and infinite unitary transformations are closely related to other mathematical concepts such as symmetry, orthogonality, and eigenvalues. They are also connected to other types of transformations, such as orthogonal and unitary matrices, which have important applications in linear algebra and geometry.