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 $v \in V$ (A)</p> Signup and view all the answers

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

<p>It is antisymmetric (A)</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 (D)</p> Signup and view all the answers

What property does the exterior product ∧ satisfy?

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

What are elements in $∧kV$ called?

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

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

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

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