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<h1> Linear Algebra</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>
<p align="left"><font color="black" size="4"><b> <br>
<a href="pdf\Time table.pdf"> Lecture schedule</a> <a href="pdf\Tutorial.pdf">Tutorial schedule</a><br><br>
<a href="pdf\seating plan (L).pdf">Seating plan during lectures</a> <a href="pdf\seating plan (T).pdf">Seating plan during tutorials</a><br><br>
</b></font>
<h2> </h2> <br>
<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="AutoNumber1" height="449">
<tr>
<td width="43%" height="449">
<p style="line-height: 10%">
<font size=4> <b>Tutorial discription</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> Content
</FONT></B> </td>
<td width="80" align="center"> <B><FONT> Problem set</FONT></B></td>
</tr>
<tr>
<td width="283"> Group, elementary matrix, row reduced echelon form, Gauss Jordan method </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\problem set 1.pdf">Problem set 1</a></b></font>
</td>
</tr>
<tr>
<td width="283"> Determinant, Vector spaces, Subspace, Basis, Dimension </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\problem set 2.pdf">Problem set 2</a></b></font>
</tr>
<tr>
<td width="283"> Linear Map and its matrix representation </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\Problem set 3.pdf">Problem set 3</a></b></font>
</tr>
<td width="283"> Inner product space </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\problem set 4.pdf">Problem set 4</a></b></font>
</tr>
<td width="283"> Eigenvalues, Eigenvectors </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\problem set 5.pdf">Problem set 5</a></b></font>
</tr>
<td width="283"> Positive and Negative definite matrices, Jordan cannonical form, Singular value decomposition </td>
<td width="80" align="center">
<font size="2"><b>
<a href="pdf\Problem set-VI.pdf">Problem set 6</a></b></font>
</tr>
</table>
<h2> </h2> <br>
<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="AutoNumber1" height="449">
<tr>
<td width="43%" height="449">
<p style="line-height: 10%">
<font size=4> <b> Assesment/Evaluation discription </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> Exam
</FONT></B> </td>
<td width="80" align="center"> <B><FONT> Tentative Marking Scheme </FONT></B></td>
</tr>
<tr>
<td width="280"> Quiz 1 (C1) </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\marking scheme q1(c1).pdf"> PDF </a></b></font>
</td>
</tr>
<tr>
<td width="280"> Quiz 2 (C1) </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\marking scheme q2(c1).pdf"> PDF </a></b></font>
</tr>
<tr>
<td width="280"> Review Test (C1) </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\marking scheme r1(c1).pdf"> PDF </a></b></font>
</tr>
<td width="280"> Quiz 1(C2) </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\marking scheme q1(c2).pdf"> PDF </a></b></font>
</tr>
<td width="280"> Review Test (C2) </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\marking scheme r1(c2).pdf"> PDF </a></b></font>
</tr>
</table>
<br><br>
<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="AutoNumber1" height="449">
<tr>
<td width="43%" height="449">
<p style="line-height: 10%">
<font size=4> <b> Computational Project </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> Exam
</FONT></B> </td>
<td width="80" align="center"> <B><FONT> Tentative Marking Scheme </FONT></B></td>
</tr>
<tr>
<td width="280"> Computational Project 1 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\lacp1(2019).pdf"> PDF </a></b></font>
</td>
</tr>
<tr>
<td width="280"> Computational Project 1 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\lacp(2019).pdf"> PDF </a></b></font>
</tr>
</table>
<br><br>
</header>
<br><br><br><br><br>
<content>
<center><h3 class="toggler-37">Marks of Linear Algebra: July - December, 2019</h3></center>
<ul class="panel-37">
<?php
if(isset($_POST['username']) && isset($_POST['password'])){
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//******************************************************
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echo "Username and Password cannot be blank.";
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elseif (ldap_bind($ldap, $dn, $password))
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$username = strtoupper($username);
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<br/>
<table class="fixed">
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<tr><td><b><u>Exam </u></b></td><td><b><u>Mark</u></b></td></tr>
</thead>
<tbody>
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<td><?php echo $data0[$c];?></td>
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<?php
}
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}
}
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<?php
}
if($flag==0)
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echo "No data found for this user. Please make sure that you are attending a valid course this semester";
}
fclose($handle);
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else
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echo "Primary data not found. Please inform at anand@iiita.ac.in";
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echo "Wrong Username/Password";
ldap_close($ds);
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<h4>Log-In using your LDAP credentials</h4>
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<label for="username">Username: </label><br>
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<input id="password" type="password" name="password" /><br><br>
<input type="submit" name="submit" value="Submit" /><br>
</form>
<?php } ?>
</ul>
</content>
<br><br><br><br><br>
<content>
<center><h3 class="toggler-37">Attendance Record of Linear Algebra: July - December, 2019</h3></center>
<ul class="panel-37">
<?php
if(isset($_POST['username']) && isset($_POST['password'])){
$adServer = "ldap://pldap.iiita.ac.in";
$ldap = ldap_connect($adServer);
$username = $_POST['username'];
$password = $_POST['password'];
ldap_set_option($ldap, LDAP_OPT_PROTOCOL_VERSION, 3);
$a = ldap_search($ldap,"dc=iiita,dc=ac,dc=in", "uid=$username");
$b = ldap_get_entries($ldap, $a);
$dn = $b[0]["dn"];
//******************************************************
if(trim($username)==='' || trim($password)==='')
{
echo "Username and Password cannot be blank.";
}
elseif (ldap_bind($ldap, $dn, $password))
{
$username = strtoupper($username);
if (($handle = fopen("attendance sheet(16-11).csv", "r")) !== FALSE)
{
$flag=0;
if((($data0 = fgetcsv($handle, 1000, ",")) !== FALSE))
{
while (($data = fgetcsv($handle, 1000, ",")) !== FALSE)
{
$num = count($data);
$fileuser = strtoupper($data[0]);
if ($num>0 && $fileuser==$username)
{
$flag = 1;
?>
<h2>Enrolment Number: <?php echo $data[0];?> Name : <?php echo $data[1];?></h2>
<br/>
<table class="fixed">
<col width="250px" />
<col width="100px" />
<thead>
<tr><td><b><u>Exam </u></b></td><td><b><u>Mark</u></b></td></tr>
</thead>
<tbody>
<?php
for ($c=2; $c < $num; $c++)
{
?>
<tr>
<td><?php echo $data0[$c];?></td>
<td><?php echo $data[$c];?></td>
</tr>
<?php
}
break;
}
}
?>
</tbody>
</table>
<?php
}
if($flag==0)
{
echo "No data found for this user. Please make sure that you are attending a valid course this semester";
}
fclose($handle);
}
else
{
echo "Primary data not found. Please inform at anand@iiita.ac.in";
}
}
else
echo "Wrong Username/Password";
ldap_close($ds);
}
else
{
?>
<h4>Log-In using your LDAP credentials</h4>
<form action="#" method="POST">
<label for="username">Username: </label><br>
<input id="username" type="text" name="username" /><br>
<label for="password">Password: </label><br>
<input id="password" type="password" name="password" /><br><br>
<input type="submit" name="submit" value="Submit" /><br>
</form>
<?php } ?>
</ul>
</content>
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