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