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Determinant: Quiz


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Question 1: These four properties can be used to compute determinants of any matrix, using ________.
LU decompositionInvertible matrixMatrix (mathematics)Gaussian elimination

Question 2: Like Lagrange, he made much use of determinants in the ________.
Number theoryMathematicsAlgebraGlossary of arithmetic and Diophantine geometry

Question 3: Under the substitution Alog(A), the ________ of A, the above equation yields det(A) = exp(tr(log(A))).
Matrix (mathematics)Logarithm of a matrixRotation matrixMatrix exponential

Question 4: The ________ CRng and Grp are related by two functors GLn and ( )×, where GLn maps any given commutative ring R to the group GLn(R), and ( )× maps any given commutative ring R to the group R×.
Ring (mathematics)Adjoint functorsInitial and terminal objectsCategory of rings

Question 5: Determinants are important both in ________, where they enter the substitution rule for several variables, and in multilinear algebra.
IntegralCalculusDifferential calculusDerivative

Question 6: Here the sum is computed over all ________ σ of the numbers {1, 2, ..., n}.
PermutationSymmetric groupGroup (mathematics)Factorial

Question 7: The determinant of a set of vectors is positive if the vectors form a right-handed ________, and negative if left-handed.
Orthogonal coordinatesCartesian coordinate systemCoordinate systemSpherical coordinate system

Question 8: This identity is used in describing the tangent space of certain matrix ________.
General linear groupLie groupGroup (mathematics)Lorentz group

Question 9: Therefore det is a ________ between GLn and ( )×.
Category theoryCategory (mathematics)Natural transformationAdjoint functors

Question 10: Alternatively one can perform the ________ if possible or the QR decomposition and find the determinant in a similar fashion.
LU decompositionMatrix (mathematics)Matrix decompositionCholesky decomposition

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