Jose's Linear Algebra Times 1

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Across
  1. 4. Difference between observed and estimated values in numerical problems.
  2. 5. Largest absolute value of the eigenvalues of a matrix.
  3. 7. Resistance of numerical algorithms to errors during computations.
  4. 10. A measure of the size or magnitude of a matrix (e.g., Frobenius norm, spectral norm).
  5. 14. Process of converting vectors into orthogonal vectors, e.g., Gram-Schmidt.
  6. 16. Method for solving linear systems by transforming the matrix into an upper triangular form.
  7. 17. An iterative algorithm to solve symmetric positive definite systems.
  8. 20. A matrix classified as positive or negative definite/semidefinite.
  9. 21. Matrix with all zeros above or below its diagonal (upper/lower triangular).
  10. 22. A system where most elements in the coefficient matrix are zero, allowing specialized solving methods.
  11. 23. A matrix divided into smaller submatrices for operations like block multiplication.
  12. 24. Symmetric matrix with all positive eigenvalues.
Down
  1. 1. A measure of the magnitude of a vector (e.g., L1 norm, L2 norm, infinity norm).
  2. 2. A matrix with a high condition number, indicating numerical instability.
  3. 3. Measure of how much the solution to a problem changes with changes in input.
  4. 6. Error caused by approximating real numbers in finite precision arithmetic.
  5. 8. A matrix where AA^T = A^T A
  6. 9. Study of changes in solutions of equations or eigenvalues when the problem is slightly altered.
  7. 11. Sensitivity of solutions to small changes in the coefficients of a system of equations.
  8. 12. Decomposition of A into lower triangular L and upper triangular U matrices.
  9. 13. Generalized inverse of a matrix, often computed using SVD.
  10. 15. Rearranging rows or columns during Gaussian elimination to enhance numerical stability.
  11. 18. Reducing a matrix's size by eliminating a known eigenvalue and eigenvector.
  12. 19. Factorization of a positive definite matrix into LL^T, where L is lower triangular.