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<h1> LAL (Summer semester), 2020</h1> <br>
<b> Objective of the course: </b> Solving systems of linear equations,
Understanding vector spaces, linear transformations, eigenvalue,
eigenvector, generalized notion of angle, distance, and length,
diagonalization and orthogonalization. <br> <br>
<b> Outcome of the course: </b> To able to solve systems of linear equations,
work within vector spaces, to manipulate matrices and to do matrix algebra.
<br> <br>
<b> Course outlines: </b> <br>
<b> Unit-I: </b> System of linear equation, Gauss elimination method,
Elementary matrices, Invertible matrices, Gauss-Jordon method for finding
inverse of a matrix, Determinant, Cramer's rule, Vector spaces, Linearly
independence and independence, Basis, Dimension. <br><br>
<b> Unit-II: </b> Linear transformation, Representation of linear maps by matrices,
Rank-Nullity theorem, Rank of a matrix, Row and column spaces, Solution space of
a system of homogeneous and non-homogeneous equations, Inner product space,
Cauchy-Schwartz inequality, Orthogonal basis. <br><br>
<b> Unit-III: </b> Grahm-Schmidt orthogonalization process, Orthogonal projection,
Eigen value, eigenvector, Cayley-Hamilton theorem, Diagonalizability and minimal
polynomial, Spectral theorem. <br><br>
<b> Unit-IV: </b> Positive, negative and semi definite matrices. Decomposition
of the matrix in terms of projections, Strategy for choosing the basis for the
four fundamental subspaces, Least square solutions and fittings, Singular values,
Primary decomposition theorem, Jordan canonical form. <br><br>
<b> Text book: </b> Gilbert Strang, Linear Algebra, Cambridge Press. <br><br>
<b> Reference books: </b> <br>
1: K. Hoffman and R. Kunze, Linear Algebra, Pearson. <br>
2: S. Kumaresan, Linear algebra - A Geometric approach, Prentice Hall of India. <br>
3: S. Lang, Introduction to Linear Algebra, Springer.
<h2> </h2> <br>
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<p style="line-height: 10%">
<font size=4> <b>LAL (Summer semester) Lecture Plan</b></font> </p>
<div align="left">
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<td height="19" align="center" width="183"> <B><FONT> Content
</FONT></B> </td>
<td width="80" align="center"> <B><FONT> Problem set</FONT></B></td>
</tr>
<tr>
<td width="283"> Group, Field </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\lecture 1.pdf">Lecture 1</a></b></font>
</td>
</tr>
<tr>
<td width="283"> System of linear equations </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\lecture 2.pdf">Lecture 2</a></b></font>
</tr>
<tr>
<td width="283"> Elementary Matrix, Row reduced echelon form </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\lecture 3.pdf">Lecture 3</a></b></font>
</tr>
<td width="283"> Invertible matrix, Gauss-Jordan method </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\lecture 4.pdf">Lecture 4</a></b></font>
</tr>
<td width="283"> Determinant </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\lecture 5.pdf">Lecture 5</a></b></font>
</tr>
<td width="283"> Vector space and subspace </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\lecture 6-7.pdf">Lecture 6-7</a></b></font>
</tr>
<td width="283"> Basis and dimension of vector space </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\lecture 8-10.pdf">Lecture 8-10</a></b></font>
</tr>
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<h2> </h2> <br>
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<p style="line-height: 10%">
<font size=4> <b> Tutorial discription </b></font> </p>
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<td height="19" align="center" width="183"> <B><FONT> Topics
</FONT></B> </td>
<td width="80" align="center"> <B><FONT> Problem Set </FONT></B></td>
</tr>
<tr>
<td width="280"> Tutorial Sheet 1 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\tutorial sheet 1.pdf"> PDF </a></b></font>
</td>
</tr>
<tr>
<td width="280"> Tutorial Sheet 2 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\tutorial sheet 2.pdf"> PDF </a></b></font>
</tr>
<tr>
<td width="280"> Tutorial Sheet 3 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\tutorial sheet 3.pdf"> PDF </a></b></font>
</tr>
<td width="280"> Tutorial Sheet 4 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\tutorial sheet 4.pdf"> PDF </a></b></font>
</tr>
<td width="280"> Tutorial Sheet 5 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\tutorial sheet 5.pdf"> PDF </a></b></font>
</tr>
</table>
<br><br>
<h2> </h2> <br>
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<p style="line-height: 10%">
<font size=4> <b> Marking Schemes </b></font> </p>
<div align="left">
<table border="1" cellpadding="2" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" width="503" id="AutoNumber2">
<tr>
<td height="19" align="center" width="183"> <B><FONT> Topics
</FONT></B> </td>
<td width="80" align="center"> <B><FONT> Problem Set </FONT></B></td>
</tr>
<tr>
<td width="280"> Review Test 1 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\review.pdf"> PDF </a></b></font>
</td>
</tr>
<tr>
<td width="280"> Review Test 2 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\review.pdf"> PDF </a></b></font>
</tr>
<tr>
<td width="280"> Review Test 3 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\review .pdf"> PDF </a></b></font>
</tr>
</table>
<br><br>
</header>
<br><br><br><br><br>
<content>
<center><h3 class="toggler-37">Marks </h3></center>
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