Exterior Algebra Quiz
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Questions and Answers

What is an element of $\wedge ^{k}V$ called?

  • Scalar product
  • Vector sum
  • k-blade (correct)
  • Multivector sum
  • What does the expression $v\wedge v$ equal to for all $v \in V$?

  • 0 (correct)
  • 1
  • $-v$
  • v
  • What is the exterior algebra of a vector space V denoted as?

  • $\wedge V$ (correct)
  • $\wedge ^{3}V$
  • $\wedge ^{k}V$
  • $\wedge ^{2}V$
  • What property does the exterior product $\wedge$ satisfy?

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

    What is the name given to elements in $\wedge kV$?

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

    What is the result of rotating a point (x, y) by an angle θ counterclockwise about the origin?

    <p>(x<em>cos(θ) - y</em>sin(θ), x<em>sin(θ) + y</em>cos(θ))</p> Signup and view all the answers

    What is the effect of rotating a vector v by an angle θ using a 2x2 rotation matrix R?

    <p>Rv</p> Signup and view all the answers

    What is the determinant of a 2x2 rotation matrix R?

    <p>1</p> Signup and view all the answers

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