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