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