高等線性代數一   (90年度 上學期)

1.Vector Spaces (including Quotient Vector Spaces, Direct Sums). 2.Linear Transformations (including Linear Functionals, Dual Space, Double Dual, Transpose of a Linear Transformation, Projections). 3.Determinants (including Alternate Multilinear Forms, Determinant Functions, Cofactors). 4.The Theory of a Single Linear Transformation (including Similarity, Eigenvalues and Eigenvectors, Characteristic and Minimal Polynomial, Rational and Jordan Forms). 5.Inner Product Spaces (including Euclidean Spaces, Unitary Spaces, Spectral Theorem). 6.Selected Topics: (a) Tensor Products. (b) Bilinear Forms. (c) Sets of Linear Transformations. (d) The Ring of Linear Transformations. (e) Infinite-Dimensional Vector Spaces.

1.Sterling K. Berberian, Linear Algebra. 2.Kenneth Hoffman and Ray Kunze, Linear Algebra. 3.Nathan Jacobson, Lectures in Abstract Algebra, vol.2, Linear Algebra.

原則上以期中考與期末考平均為準。