# Vector space: Quiz

Question 1: Vectors were reconsidered with the presentation of ________ by Argand and Hamilton and the inception of quaternions by the latter.
Complex numberField (mathematics)Real numberVector space

Question 2: For example, the ________ consists of the collection of tangent spaces parametrized by the points of a differentiable manifold.
Vector bundleFiber bundleVector spaceTangent bundle

Question 3: Actually Grassmann's 1844 work exceeds the framework of vector spaces, since his considering multiplication, too, led him to what are today called ________.
AlgebraGroup (mathematics)Algebraic structureMathematics

Question 4: To qualify as a vector space, addition and multiplication have to adhere to a number of requirements called ________.
AxiomAxiomatic systemMathematical logicSet theory

Question 5: [81] The concrete formulae above are consequences of a more general mathematical duality called ________.
Topological groupLocally compact spaceFourier transformPontryagin duality

Question 6: Forcing two such elements to be equal leads to the symmetric algebra, whereas forcing v1v2 = − v2v1 yields the ________.
Representation theoryVector spaceClifford algebraExterior algebra

Question 7: Likewise, linear algebra is not adapted to deal with ________, since the addition operation allows only finitely many terms to be added.
Taylor seriesMathematical analysisSeries (mathematics)Compact space

Question 8: Coordinate space Fn can be equipped with the standard ________:
Vector spaceCross productEuclidean vectorDot product

Question 9:
Which of the following titles did Vector space have?
 The Plane Makers Tangent Line EverQuest: The Planes of Power Tangent plane

Question 10: A field is, essentially, a set of numbers possessing ________, subtraction, multiplication and division operations.