201 Phys
1) Systems of linear equations and matrices: Introduction to systems of
linear equations, Gaussian elimination, Homogeneous Systems of linear
equations, Matrices and matrix operations, Rules of matrix arithmetic,
Elementary matrices and a method for finding inverse A.
2) Determinants: The determinant function, Evaluating determinants by row
reduction, Properties of the determinant function, Cofactor expansion,
Cramer's rule.
3) Vectors 2d-space and 3d-space: Introduction to vectors (Geometric),
Norm of a vector; vector arithmetic, Dot product; projections, Cross
product.
4) Vector spaces: Euclidean n-space, General vector spaces, Subspaces,
Linear independence, Basis and dimension, Row and column space of a
matrix; rank; Application to finding bases, Inner product spaces; length
and angle in inner product spaces, Orthonormal basis; Gram-Schmidt
process, Coordinates; change of basis.
5) Linear transformations: Introduction to linear transformations,
Properties of linear transformation: Kernel and Range.
6) Eigenvalues and eigenvectors: Eigenvalues and eigenvectors,
Diagonalization, Orthogonal Diagonalization.
Text Book:
Howard Anton, Elementary Linear Algebra, 11th edition, John Wiley & Sons, Inc.