8 Questions
What is an element of $\wedge ^{k}V$ called?
k-blade
What does the expression $v\wedge v$ equal to for all $v \in V$?
0
What is the exterior algebra of a vector space V denoted as?
$\wedge V$
What property does the exterior product $\wedge$ satisfy?
Alternating property
What is the name given to elements in $\wedge kV$?
k-multivectors
What is the result of rotating a point (x, y) by an angle θ counterclockwise about the origin?
(xcos(θ) - ysin(θ), xsin(θ) + ycos(θ))
What is the effect of rotating a vector v by an angle θ using a 2x2 rotation matrix R?
Rv
What is the determinant of a 2x2 rotation matrix R?
1
Test your knowledge of exterior algebra with this quiz. Explore the graded associative algebra ∧V = k ⊕ V ⊕ ∧2V ⊕ ∧3V ⊕ ⋯ and the exterior product or wedge product. Sharpen your understanding of elements and operations within the exterior algebra of a vector space.
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