MTH 230 LINEAR ALGEBRA

1. Systems of Linear Equations

1.1 Two linear equations in two unknowns

1.2 Gauss and GaussJordan elimination

1.3 Homogeneous systems of equations

2. Vectors and Matrices

2.1 Vectors and scalar products

2.2 Matrices and matrix products

2.3 Matrices and linear systems of equations

2.4 Linear independence and Homogeneous systems

2.5 Matrix inverse

2.6 Matrix Transpose

3. Determinants

3.1 The determinant function

3.2 Properties of the determinant

3.3 Determinants and inverses

3.4 Cramer's Rule

4. Vector Spaces

4.1 Definition and basic properties

4.2 Subspaces

4.3 Linear independence and linear combinations

4.4 Bases and dimension

4.5 Change of bases

4.6 Orthonormal bases and projection

5. Linear Transformations

5.1 Definition and examples

5.2 Properties of linear transformations

5.3 Range and kernel

5.4 Rank and nullity

5.5 Matrix of a transformation

6. Eigenvalues, Eigenvectors, and Canonical Forms

6.1 Eigenvalues and Eigenvectors

6.2 Similar matrices and diagonalization

6.3 Symmetric matrices and orthogonal diagonalization

6.4 Quadratic forms

6.5 CayleyHamilton theorem and spectral theorem

7. Numerical Methods

7.1 Gaussian elimination

7.2 Eigenvalues and Eigenvectors

7.3 Error in numerical computations

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