A) A single linear sequence of numbers B) A circular array of numbers C) A rectangular array of numbers or other mathematical objects D) A three-dimensional cube of numbers
A) In rows and columns B) In random clusters C) In concentric circles D) In hierarchical trees
A) A 3 by 2 matrix B) A square matrix C) A 2 by 3 matrix D) An empty matrix
A) Probability distributions B) Prime numbers C) Geometric points D) Linear maps
A) For geometric transformations and coordinate changes B) To measure lengths of curves only C) To define continuous functions D) To calculate the area of circles
A) Infinite matrices B) Square matrices C) Row matrices D) Empty matrices
A) A row vector B) An empty matrix C) An infinite matrix D) A square matrix
A) If and only if it has a nonzero determinant B) If and only if all its entries are negative C) If and only if its determinant is zero D) If and only if it has more rows than columns
A) The number of rows it contains B) The sum of its diagonal entries C) The product of its dimensions D) The roots of its characteristic polynomial
A) Fluid dynamics and thermodynamics B) Calculus, topology, and number theory only C) Quantum mechanics exclusively D) Graph theory, algebra, combinatorics, and statistics
A) Nodes or vertices B) Entries or elements C) Roots or powers D) Factors or multiples
A) Rows B) Vectors C) Diagonals D) Columns
A) Scalers B) Rows C) Columns D) Diagonals
A) By the largest number in the matrix B) By the number of rows and columns it contains C) By the sum of all its entries D) By the value of its determinant
A) They must be prime numbers B) They must be positive integers C) They must be even numbers D) They must be equal
A) A square matrix B) An infinite matrix C) An n by m matrix D) An m by n matrix
A) Column matrices B) Square matrices C) Diagonal matrices D) Row matrices or row vectors
A) Empty matrices B) Row matrices C) Column matrices or column vectors D) Square matrices
A) An undefined matrix B) A giant matrix C) An infinite matrix D) A limitless matrix
A) An empty matrix B) A null matrix C) A blank matrix D) A zero matrix
A) Computer algebra programs B) Physical measurement C) Manual arithmetic calculations D) Geometric drawing by hand
A) Double vertical bars B) Curly braces or angle brackets C) Single vertical bars D) Square brackets or parentheses
A) Using upper-case letters B) Using lower-case Greek letters C) Using symbols like asterisks D) Using numbers
A) Using corresponding lower-case letters with two subscript indices B) Using Roman numerals C) Using upper-case letters with exponents D) Using bold numbers
A) Boldface roman B) Italicized lowercase C) Underlined lowercase D) Superscripted text
A) A tilde above the letter B) A dashed box around the letter C) A circle surrounding the letter D) A double-underline with the variable name
A) The entry in the ith row and jth column B) The sum of row i and column j C) The product of dimension i and j D) The determinant of the submatrix
A) Sq(m, n) B) R(m, n) C) Mat(R) D) M(m, n)
A) R_n(M) B) F_n(R) C) Mat(n, R, m) D) M_n(R)
A) By multiplying determinants B) Columnwise from right to left C) Using row reduction D) Entrywise
A) Matrix B) Vector C) Tensor D) Scalar
A) Scalar product B) Dot product C) Inner product D) cA
A) Scalar multiplication B) Matrix subtraction C) Inner product D) Matrix addition
A) AT B) |A| C) A* D) A-1
A) A B) AT C) -A D) 2A
A) (A + B)T = ATBT B) (A + B)T = A + BT C) (A + B)T = AT + BT D) (A + B)T = AT + B
A) Composition B) Transposition C) Inversion D) Addition
A) Invertibility for all matrices B) Commutativity C) Division D) Associativity
A) Yes B) No C) Only for non-square matrices D) Only when matrices are zero
A) (AB)C = A(BC) B) AB + C = A + BC C) (AB)C = (AC)B D) A(BC) = (BA)C
A) C(A + B) = AC + CB B) C(A + B) = CA + BC C) (A + B)C = AB + C D) (A + B)C = AC + BC
A) Sylvester equation B) Differential equation C) Quadratic equation D) Linear algebraic equation
A) A fractional constant only B) Any constant including zero C) A non-zero constant D) A negative constant
A) LU decomposition B) Gauss–Jordan elimination C) Gauss elimination D) Cramer's rule
A) Determinant expansion B) Matrix inversion C) Gauss–Jordan elimination D) Gauss elimination
A) Identity submatrix B) Leading principal submatrix C) Minor submatrix D) Diagonal submatrix
A) A rhombus B) A parallelogram C) A rectangle D) A trapezoid
A) B - A B) A + B C) AB D) BA
A) The kernel B) The image C) The codomain D) The domain
A) A scalar multiple B) The identity section C) The main diagonal D) An upper triangular part
A) On the line running from the bottom left to the top right B) On the imaginary line running from the top left corner to the bottom right corner C) Along the bottom row D) Along the rightmost column
A) An integral domain B) A noncommutative ring C) A linear vector space D) A commutative field
A) AB = I B) A* = A C) A = AT D) A = -AT
A) Conjugate transpose B) Inverse matrix C) Determinant D) Regular transpose
A) Quadratic form theorem B) Spectral theorem C) Invertible matrix theorem D) Gaussian elimination
A) All eigenvalues are complex B) All eigenvalues are real C) All eigenvalues are zero D) All eigenvalues are negative
A) Singular B) Skew-symmetric C) Indefinite D) Non-singular
A) A* B) An C) AT D) A-1
A) Negative-definite B) Indefinite C) Skew-symmetric D) Positive-definite
A) Negative-definite B) Positive-semidefinite C) Positive-definite D) Negative-semidefinite
A) Identity vector xi B) Conjugate transpose xH C) Negative transpose -xT D) Inverse transpose x-1
A) Hermitian form B) Sesquilinear form C) Quadratic form D) Bilinear form
A) Yes B) Only for non-square matrices C) No D) Only if the determinant is zero
A) Pure reflection without rotation B) Pure rotation without reflection C) Shear mapping D) Scaling
A) Preserves the orientation B) Doubles the orientation C) Destroys the orientation D) Reverses the orientation
A) A = A-1 B) AT A = I C) det(A) = 1 D) A*A = AA*
A) Eigenvector B) Matrix product C) Determinant D) Eigenvalue
A) Eigenvalue B) Characteristic polynomial C) Eigenvector D) Zero matrix
A) Always zero B) Complex C) Undefined D) Always real
A) Static approaches B) Random approaches C) Recursive approaches D) Iterative approaches
A) Elementary operations B) Sparse entries C) Determinants D) Eigenvalues
A) MapReduce algorithm B) Cayley-Hamilton algorithm C) Conjugate gradient method D) Strassen algorithm
A) Adjunc B) Eigen-solver C) Numerical linear system D) MapReduce
A) A - lambda In B) det(A) / adj(A) C) A times det(A) D) adj(A) / det(A)
A) Ill-conditioned B) Triangular C) Diagonalizable D) Unitary
A) Jordan decomposition B) Schur decomposition C) Gaussian elimination D) LU decomposition
A) At most one thousand B) Exclusively square dimensions C) Infinitely many D) Only finite numbers
A) Vectors B) Tensors C) Determinants D) Scalars
A) A category B) A field C) A group D) A vector space
A) A ring B) A field C) A group D) A module
A) Polynomials B) Tensors C) Categories D) Vectors
A) Categories B) Matrix fields C) Rings D) Vector spaces
A) Scalars B) Bases C) Eigenvalues D) Determinants
A) A matrix B) A determinant C) A representation D) A group
A) Subgroup B) Determinant C) Transpose D) Supergroup
A) The special linear group B) The symmetric group C) The special orthogonal group D) The general linear group
A) Combinatorial topology B) Arithmetic geometry C) Functional analysis D) Elementary algebra
A) The Leibniz formula B) The commutative monoid identity C) The functional analysis identity D) The Desnanot–Jacobi identity
A) A field B) A Hilbert space C) A commutative monoid D) A semiring
A) A vector space B) A group C) A commutative monoid D) A semiring
A) Finitary permutations B) Even permutations C) All permutations D) Odd permutations
A) Even permutations B) Zero permutations C) Odd permutations D) All permutations
A) Identity morphisms B) Coproducts C) Tensor products D) Initial objects
A) Epimorphisms B) Zero morphisms C) Monomorphisms D) Isomorphisms
A) Categories B) Vector spaces C) Functors D) Sets
A) The tensor unit I B) The initial object C) The empty set D) The tensor product
A) The identity set B) The tensor unit I C) A canonical isomorphism D) The initial object
A) The Caesar cipher B) The RSA algorithm C) The Enigma machine D) The Hill cipher
A) The minimax method B) The Hartree–Fock method C) The Hill cipher method D) The affine projection method
A) Game theory minimax equations B) Linear programming equations C) The Roothaan equations D) Complex number equations |