preface
matrices and systems of equations
1.1 systems of linear equations
1.2 row echelonform
1.3 matrix arithmetic
1.4 matrix algebra
1.5 elementary matrices
1.6 partitioned matrices
matlab r exercises
chaptertesta
chaptertestb
2 determinants
2.1 the determinant of a matrix
2.2 properties of determinants
2.3. additionaltopics and applications
matlab exercises
chaptertesta
chaptertestb
3 vector spaces
3.1 definition and examples
3.2 subspaces
3.3 linear independence
3.4 basis and dimension
3.5 change of basis
3.6 row space and column space
matlab exercises
chaptertesta
chaptertestb
4 linear transformations
4.1 definition and examples
4.2 matrix representationsof lineartransformations
4.3 similarity
matlab exercises
chaptertesta
chaptertestb
5 orthogonality
5.1 the scalar product in rn
5.2 orthogonal subspaces
5.3 least squares problems
5.4 inner product spaces
5.5 orthonormal sets
5.6 the gram–schmidt orthogonalization process
5.7 orthogonal polynomials
matlab exercises
chaptertesta
chaptertestb
6 eigenvalues
6.1 eigenvalues and eigenvectors
6.2 systems of linear differential equations
6.3 diagonalization
6.4 hermitian matrices
6.5 the singularvalue decomposition
6.6 quadraticforms
6.7 positive definite matrices
6.8 nonnegative matrices
matlab exercises
chaptertesta
chaptertestb
7 numerical linear algebra
7.1 floating-point numbers
7.2 gaussian elimination
7.3 pivoting strategies
7.4 matrix norms and condition numbers
7.5 orthogonal transformations
7.6 the eigenvalue problem
7.7 least squares problems
matlab exercises
chapter test a
chapter test b
8 iterative methods web.
9 canonical forms web.
appendix: matlab
bibliography
answers to selected exercises
index
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