What Do You Know About Real Representations?

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Quizzes Created: 129 | Total Attempts: 42,271
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  • 1/10 Questions

    How do we represent complex vector space?

    • V
    • U
    • S
    • R
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About This Quiz

In mathematics--especially when considering the field of representation theory on a vector space represented by an invariant real structure, real representations are very useful. If you are willing to learn more about this theorem or get more information associated with it, consider this quiz and ensure that you practice the questions.

What Do You Know About Real Representations? - Quiz

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  • 2. 
    What is the invariant real structure also termed as?  - ProProfs

    What is the invariant real structure also termed as? 

    • Antilinear equivariant map

    • Linear equivariant map

    • Stability

    • Control of vehicles flying through air

    Correct Answer
    A. Antilinear equivariant map
    Explanation
    The invariant real structure is also known as an antilinear equivariant map. This term refers to a mapping that preserves the real structure of a mathematical object while also respecting certain symmetry properties. In this context, the term "antilinear" indicates that the map preserves the complex conjugation operation, while "equivariant" means that it respects the symmetries of the object being mapped. Overall, this term is used to describe a specific type of mapping that has both antilinear and equivariant properties.

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  • 3. 
    In the subject of physics, representations are viewed as what? - ProProfs

    In the subject of physics, representations are viewed as what?

    • Matrices

    • Momentum

    • Inertia

    • Space

    Correct Answer
    A. Matrices
    Explanation
    In the subject of physics, representations are viewed as matrices. Matrices are mathematical structures that are used to represent physical quantities and relationships between them. In physics, matrices are commonly used to represent transformations, such as rotations or translations, as well as to describe the behavior of physical systems. They allow physicists to analyze and manipulate complex physical phenomena using mathematical tools. Therefore, matrices are an important tool in the study and understanding of physics.

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  • 4. 
    What is the descriptive feature of a Hermitian form?  - ProProfs

    What is the descriptive feature of a Hermitian form? 

    • Representation changes to a degenerate invariant linear form

    • Representation changes to a nondegenerate invariant sesquilinear form

    • Representation changes to the linear form

    • Representation changes to the sesquilinear form

    Correct Answer
    A. Representation changes to a nondegenerate invariant sesquilinear form
    Explanation
    A Hermitian form is a complex-valued bilinear form that satisfies a certain symmetry property. The descriptive feature of a Hermitian form is that its representation changes to a nondegenerate invariant sesquilinear form. This means that the form remains bilinear and satisfies certain symmetry conditions, but it is also nondegenerate, meaning that it has no nontrivial null vectors. Additionally, the form is invariant under certain transformations, meaning that it remains unchanged when the underlying vector space is transformed.

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  • 5. 
    The representation of symmetric groups are... - ProProfs

    The representation of symmetric groups are...

    • Irrational

    • Real

    • Complex

    • Rational

    Correct Answer
    A. Real
    Explanation
    The representation of symmetric groups can be classified as real because the elements of these groups can be represented by real numbers. Unlike complex numbers, which have both real and imaginary parts, the representations of symmetric groups only involve real values. This classification is important in the study of group theory and helps understand the properties and behavior of symmetric groups.

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  • 6. 
    How do we represent real vector space?  - ProProfs

    How do we represent real vector space? 

    • V

    • U

    • S

    • R

    Correct Answer
    A. U
    Explanation
    In mathematics, a real vector space is represented by the symbol U.

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  • 7. 
    A representation on a complex vector space is isomorphic to what? - ProProfs

    A representation on a complex vector space is isomorphic to what?

    • Dual representation

    • Single representation

    • Complete representation

    • Multiple representation

    Correct Answer
    A. Dual representation
    Explanation
    A representation on a complex vector space is isomorphic to the dual representation because the dual representation is the set of all linear transformations from the original representation to the complex numbers. This means that the dual representation captures all the information and structure of the original representation, making it isomorphic to the complex vector space.

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  • 8. 
    What happens to the direct sum of quaternionic and real representation? - ProProfs

    What happens to the direct sum of quaternionic and real representation?

    • Real

    • Neither real nor quaternionic

    • Both real and quaternionic

    • Quaternionic

    Correct Answer
    A. Neither real nor quaternionic
    Explanation
    When we take the direct sum of a quaternionic representation and a real representation, the resulting representation is neither purely real nor purely quaternionic. The direct sum combines the two representations into a single representation where each element is a pair consisting of a quaternionic element and a real element. Thus, the resulting representation contains both quaternionic and real components.

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  • 9. 
    The representation of a Hermitian form is also referred to as what? - ProProfs

    The representation of a Hermitian form is also referred to as what?

    • Pseudo hermitian

    • Real hermitian

    • Universal hermitian

    • Concurrent hermitian

    Correct Answer
    A. Pseudo hermitian
    Explanation
    A Hermitian form is a complex-valued function that satisfies certain properties. The representation of a Hermitian form that is referred to as "pseudo hermitian" means that it possesses similar properties to a Hermitian form but may not satisfy all of them. This term is used to describe a generalized or approximate version of a Hermitian form.

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  • 10. 
    The representation of rotational groups are... - ProProfs

    The representation of rotational groups are...

    • Complex

    • Rational

    • Irrational

    • Real

    Correct Answer
    A. Real
    Explanation
    The representation of rotational groups can be described as real. This is because the elements of a rotational group can be represented by real numbers, such as angles or coordinates in three-dimensional space. Unlike complex, rational, or irrational numbers, which may not accurately represent the rotational transformations, real numbers provide a suitable and practical representation for rotational groups.

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  • Mar 20, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Jul 22, 2018
    Quiz Created by
    AdeKoju
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