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\begin{document}
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\begin{center}

  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2020--21--B term}\\[0.2\baselineskip]

\end{center}

\begin{description}
  \item[Course Name]
    Linear Algebra ME

  \item[Course Number]
    \LRE{201‭.1‭.9321}

  \item[Course web page]\mbox{}\\
    \url{https://www.math.bgu.ac.il//en/teaching/spring2021/courses/linear-algebra-me}

  \item[Lecturer]
    Prof. Mikhail  Muzychuk,
    \nolinkurl{<muzychuk@bgu.ac.il>},
    Office 305

\item[Office Hours]
  \url{https://www.math.bgu.ac.il/en/teaching/hours}
\end{description}

\section*{Abstract}




\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}






\section*{Course topics}

\begin{enumerate}
\item{} The real numbers, inequalities in real numbers, the complex numbers, the Cartesian
representation, the polar representation, the exponential representation, the Theorem of de
Moivre, root computations.
\item{} Systems of linear equations over the real or complex numbers, the solution set and its
parametric representation, echelon form and the reduced echelon form of a matrix, backwards
substitution, forward substitution and their complexity, the Gauss elimination algorithm and its
complexity, the reduction algorithm and its complexity.
\item{} Vector spaces, sub-spaces of vector spaces, linear combinations of vectors, the span of a set
of vectors, linear dependence and linear independence, the dimension of a vector space, row
spaces and column spaces of matrices, the rank of a matrix.
\item{} Linear mappings between vector spaces, invertible mappings and isomorphisms, the matrix
representation of finite dimensional linear mappings, inversion of a square matrix, composition
of mappings, multiplication of matrices, the algebra of matrices, the kernel and the image of a
linear mapping and the computation of bases, changing of a basis, the dimension theorem for
linear mappings.
\item{} Inner product spaces, orthogonality, the norm of a vector, orthonormal sets of vectors, the
Cauchy-Schwarz inequality, the orthogonal complement of a sub-space, orthogonal sequences
of vectors, the Gram-Schmidt algorithm, orthogonal transformations and orthogonal matrices.
\item{} The determinant of a square matrix, minors and cofactors, Laplace expansions of the
determinant, the adjoint matrix and Laplace theorem, conjugation of a square matrix, similarity
transformations and their invariants (the determinant and the trace).
\item{} Eigenvalues, eigenvectors, eigenspaces, diagonalization and similarity, the characteristic
polynomial, the algebraic and the geometric multiplicities of an eigenvalue, the spectral
theorem for Hermitian matrices.
\end{enumerate}

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\end{document}

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