Exterior Algebra and Wedge Product Quiz
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Questions and Answers

What is an element of the exterior algebra ∧V called when it is a sum of elements $v_1\wedge...\wedge v_k$, where $v_i \in V$?

  • k-blade (correct)
  • Scalar
  • Basis
  • Vector
  • What is the algebraic structure of the exterior algebra of a vector space V?

  • Graded associative algebra (correct)
  • Scalar multiplication
  • Linear transformation
  • Vector field
  • What are elements in ∧kV called?

  • Tensors
  • k-multivectors (correct)
  • Matrices
  • Scalars
  • What property does the exterior product ∧ satisfy?

    <p>Alternating property: $v\wedge v = 0$ for all $v \in V$</p> Signup and view all the answers

    What does the property u∧v = - v∧u imply about the exterior product ∧?

    <p>It is antisymmetric</p> Signup and view all the answers

    What is the algebraic structure of the exterior algebra of a vector space V?

    <p>Graded associative algebra</p> Signup and view all the answers

    What property does the exterior product ∧ satisfy?

    <p>Alternating property: $vigwedge v = 0$ for all $v ext{ in } V$</p> Signup and view all the answers

    What are elements in $∧kV$ called?

    <p>k-multivectors</p> Signup and view all the answers

    What does the property $uigwedge v = - vigwedge u$ imply about the exterior product $∧$?

    <p>Antisymmetric property</p> Signup and view all the answers

    What is an element of the exterior algebra $∧V$ called when it is a sum of elements $v_1igwedge...igwedge v_k$, where $v_i ext{ in } V$?

    <p>k-blade</p> Signup and view all the answers

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