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\centerline {\largerbold  640:250 Introduction to Linear Algebra
      }
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{\bf Text:} Spence, Insel \& Friedberg {\sl Elementary Linear Algebra: A
   Matrix Approach, 2nd Edition}

\ \ \ \ \ \ ISBN \# 978-0-13-187141-0, Prentice-Hall, Upper Saddle River, NJ 07458
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\centerline {\largerbold  Syllabus }

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     & {\bf Lecture} & {\bf Reading} & {\bf Topics}\cr
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     & 1 &1.1, 1.2 & Matrices, Vectors, and Linear Combinations   \cr\\ 
     & 2 &1.3 & Systems of Linear Equations; Reduced Row Echelon Form \cr\\
     & 3 &1.4 & Gaussian Elimination; Rank and Nullity of a Matrix \cr\\
     & 4 &1.6  & Span of a Set of Vectors \cr \\	
     & 5 &1.7 &  Linear Dependence and Linear Independence \cr\\
     & 6  &1.7, 2.1 & Homogeneous Systems; Matrix Multiplication \cr\\
     & 7 & 2.1 & Matrix Algebra  \cr\\ 
     & 8 & 2.3 & Invertibility and Elementary Matrices; \cr\\
     & & & Column Correspondence Property \cr\\
     &  & App. E & Uniqueness of Reduced Row Echelon Form \cr\\
     & 9 &2.4 & Inverse of a Matrix \cr \\
   &  & 2.5 & Partitioned Matrices and Block Multiplication \cr \\
   & 10 &2.6  & $LU$ Decomposition of a Matrix \cr\\
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   & 11 & \multispan 2 $\!\!${\bf Midterm Exam \#1 }  \hfill \cr\\
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   & 12 & 3.1 & Determinants; Cofactor Expansions  \cr\\ 
   & 13 & 3.2 & Properties of Determinants \cr \\ 
   & 14 & 4.1 & Subspaces \cr\\
   & 15 & 4.2 & Basis and Dimension \cr\\ 
   & 16 & 4.3 & Column Space, Null Space and Row Space of a Matrix  \cr\\ 
   & 17 & 5.1 & Eigenvalues and Eigenvectors  \cr\\
   & 18 & 5.2 & Characteristic Polynomial  \cr \\
   & 19 & 5.3 & Diagonalization of a Matrix \cr\\
   & 20 & 5.5 & Examples of Diagonalization  \cr\\ 
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   & 21 & \multispan 2 $\!\!${\bf Midterm Exam \# 2}  \hfill \cr\\
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   & 22 & 6.1 & Geometry of Vectors; Projection onto a Line \cr\\
   & 23 & 6.2 & Orthogonal Sets of Vectors;  \cr\\
   &    &     & Gram-Schmidt Process; $QR$ factorization \cr\\
   & 24 & 6.3 & Orthogonal Projection; Orthogonal Complements
   \cr\\
   &    &     & Projection onto Column Space; Closest Vector Property \cr\\
   & 25 & 6.4 & Least Squares Method; Normal Equations; Solving
   Inconsistent Systems  \cr\\
   & 26 &  6.5, 6.6 & Orthogonal Matrices; Diagonalization of Symmetric Matrices  \cr\\ 
   & 27 & 6.6 &  Diagonalization of Quadratic Forms \cr\\ 
   &    &     & Spectral Decomposition for Symmetric Matrices \cr\\
   & 28 & & Catch up and review \cr\\
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   &  & \multispan 2 $\!\!${\bf Final  Exam } \quad (Class Hour Schedule)
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