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1553Shared-Factor Spectrum 3A = 1I + 211 T in dimension n=3. What are its eigenvalues?数学中等数值题未尝试免费1554Ridge Plus Crowd Mode 4A = 4I + 1/211 T in dimension n=6. What are its eigenvalues?数学中等derivation未尝试免费1556Mode-Weighted Matrix Power 1A diagonalizable matrix satisfies Au 1 = 5u 1 and Au 2 = 2u 2. If v = 1u 1 + -1u 2, what is A 3v?数学简单数值题未尝试免费1557Two-Mode Propagation 2A diagonalizable matrix satisfies Au 1 = 4u 1 and Au 2 = 1u 2. If v = 2u 1 + 3u 2, what is A 4v?数学中等derivation未尝试免费1558Diagonalizable Shock Propagation 3A diagonalizable matrix satisfies Au 1 = 3u 1 and Au 2 = 6u 2. If v = -1u 1 + 2u 2, what is A 2v?数学中等数值题未尝试免费1561Averaging Residual Decay 1A linear operator has dominant eigenvalue 1 and second eigenvalue 4/5. If an initial deviation from consensus is 10, what is the remaining deviation after 3 applications along that second mode?数学简单数值题未尝试免费1566Trace-and-Square Inference 1A 2x2 matrix has eigenvalues 4 and lambda. Its trace is 10. What is lambda?数学简单数值题未尝试免费1571Rank-One Spectrum Description 1A rank-one symmetric matrix has eigenvalue 7 along the ones direction. What are the remaining eigenvalues along all vectors orthogonal to 1?数学简单数值题未尝试免费1576Ridge Needed to Cap a Condition Number 1A symmetric positive definite matrix has eigenvalues 1 and 13. Before inverting it, a desk adds lambda I. What is the smallest nonnegative lambda that makes the condition number of A + lambda I at most 4?数学简单数值题未尝试免费1578Ridge Needed to Cap a Condition Number 3A symmetric positive definite matrix has eigenvalues 0.5 and 8. Before inverting it, a desk adds lambda I. What is the smallest nonnegative lambda that makes the condition number of A + lambda I at most 5?数学中等derivation未尝试免费1579Ridge Needed to Cap a Condition Number 4A symmetric positive definite matrix has eigenvalues 1.5 and 10.5. Before inverting it, a desk adds lambda I. What is the smallest nonnegative lambda that makes the condition number of A + lambda I at most 2.5?数学中等数值题未尝试免费1580Ridge Needed to Cap a Condition Number 5A symmetric positive definite matrix has eigenvalues 0.8 and 15.2. Before inverting it, a desk adds lambda I. What is the smallest nonnegative lambda that makes the condition number of A + lambda I at most 6?数学困难derivation未尝试面试订阅1581Worst-Case Curvature of a Coupled Penalty 1Consider q(x,y) = 3x 2 + 4xy + 8y 2. What is the largest real number m such that q(x,y) >= m(x 2 + y 2) for every pair (x,y)?数学简单数值题未尝试免费1582Worst-Case Curvature of a Coupled Penalty 2Consider q(x,y) = 5x 2 - 6xy + 5y 2. What is the largest m such that q(x,y) >= m(x 2 + y 2) for all (x,y)?数学中等derivation未尝试免费1583Cross-Term Budget Under a Curvature Floor 3For q(x,y) = 4x 2 + 2kxy + 7y 2, what is the largest absolute value |k| such that q(x,y) >= 2(x 2 + y 2) for all (x,y)?数学中等数值题未尝试免费1584Minimum Unit-Norm Penalty 4What is the minimum value of 6x 2 + 8xy + 10y 2 over all vectors satisfying x 2 + y 2 = 1?数学中等derivation未尝试免费1585One-Sided Diagonal Repair 5For what smallest u does the quadratic form (1+u)x 2 + 4xy + 5y 2 stay nonnegative for all (x,y)?数学困难derivation未尝试面试订阅1586Eliminate One Coordinate of a Quadratic 1Consider q(x,y) = 4x 2 + 6xy + 5y 2. If y is chosen optimally for each fixed x, what coefficient multiplies x 2 in the reduced one-variable penalty?数学简单derivation未尝试免费1587Eliminate One Coordinate of a Quadratic 2Consider q(x,y) = 7x 2 + -4xy + 3y 2. If y is chosen optimally for each fixed x, what coefficient multiplies x 2 in the reduced one-variable penalty?数学简单数值题未尝试免费1589Pick the Residual Variance in a Schur Reduction 4A coupled penalty is q(x,y) = 10x 2 + 12xy + cy 2. After optimizing out y, the desk wants the remaining x 2 coefficient to be exactly 6. What value of c is required?数学困难数值题未尝试面试订阅