The Computational Solutions from Introduction to Linear Algebra: Third Edition

by Gilbert Strang.

Chapter 1 (Introduction to Vectors):

• prob_1_1_1.m (plots of some simple vectors)
  
• prob_1_1_2.m (plots of some simple vectors)
  
• prob_1_1_9.m (some simple parallelograms)
  
Chapter 2 (Solving Linear Systems):

• prob_2_1_30.m (iterating Markov matrices)
  
• prob_2_1_32.m (plots of the iterates of Markov matrices)
  
• prob_2_5_33.m (the exact versus numerical inverse of Hilbert matrices)
  
• prob_2_6_23.m (LU decompositions of pascal matrices)
  
  • slu.m (Requires Strang's textbook LU factorization (without row exchanges))
    
• prob_2_6_25.m (slu converted into sldu)
  
• prob_2_6_26.m (slu by overwriting the original matrix)
  
• prob_2_6_28.m (multiply a lower triangular matrix by a upper triangular matrix)
  
• prob_2_7_26.m (splu converted into spldu)
  
Chapter 3 (Vector Spaces and Subspaces):

• There were no computational problems for this chapter
Chapter 4 (Orthogonality):

• prob_4_4_27.m (simple implementation of the QR factorization)
  
Chapter 5 (Determinants):

• There were no computational problems for this chapter
Chapter 6 (Eigenvalues and Eigenvectors):

• prob_6_4_27.m (symmetry of a computed projection matrix)
  
Chapter 7 (Linear Transformations):

• prob_7_1_22.m (the "house" for various matrices)
  
• prob_7_1_26.m (the "house" with a chimney)
  
• prob_7_1_27.m (mapping two dimensional regions with linear transformation)
  
• prob_7_1_28.m (further mapping two dimensional regions)
  
• prob_7_1_29.m (linear transformation of the "house")
  
Chapter 8 (Applications):

• There were no computational problems for this chapter
Chapter 9 (Numerical Linear Algebra):

• prob_9_1_2.m (ill-conditioning of the Hilbert matrices)
  
• prob_9_1_3.m (ill-conditioning of the Hilbert matrices continued)
  
• prob_9_1_4.m (ill-conditioning of the Hilbert matrices continued again)
  
• prob_9_1_10.m (the possible accuracy errors possible by performing LU without pivoting)
  
  • slu.m (Requires Strang's textbook LU factorization (without row exchanges))
    
  • slv.m (Requires Strang's textbook LU backsolve (without row exchanges))
    
• prob_9_2_9.m (eigenvalue calculations for this problem)
  
• prob_9_2_11.m (eigenvalue calculations for this problem)
  
• prob_9_3_10.m (the Gauss-Seidel method on the -1, 2, -1 matrix)
  
• prob_9_3_12.m (the SOR method on the -1, 2, -1 matrix)
  
• prob_9_3_14.m (the inverse power method with a Markov matrix)
  
• prob_9_3_17.m (the inverse power method again)
  
• prob_9_3_22.m (a demonstration of the Lanczos algorithm on the -1, 2, -1 matrix)
  
• The problems above may require the core numeric algorithms below
  
  • gen_der2_mat.m (a simple function to construct the -1, 2, -1 matrix easily)
    
  • jacobi.m (An implementation of the Jacobi iterative method to solve Ax=b)
    
  • gseidel.m (An implementation of the Gauss-Seidel iterative method to solve Ax=b)
    
  • sor.m (An implementation of the SOR iterative method to solve Ax=b)
    
  • lanczos.m (An implementation of the Lanczos algorithm)
    
Chapter 10 (Complex Vectors and Matrices):

• There were no computational problems for this chapter