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<title>2. Linear Algebra, Handling of Arrays and more Python Features &#8212; Applied Data Analysis and Machine Learning</title>
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About the course
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@@ -116,7 +122,7 @@ const thebe_selector_output = ".output, .cell_output"
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Review of Statistics with Resampling Techniques and Linear Algebra
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@@ -133,7 +139,7 @@ const thebe_selector_output = ".output, .cell_output"
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From Regression to Support Vector Machines
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@@ -170,7 +176,7 @@ const thebe_selector_output = ".output, .cell_output"
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Decision Trees, Ensemble Methods and Boosting
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Dimensionality Reduction
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Deep Learning Methods
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@@ -299,7 +305,7 @@ const thebe_selector_output = ".output, .cell_output"
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@@ -358,7 +364,69 @@ const thebe_selector_output = ".output, .cell_output"
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<h1>Linear Algebra, Handling of Arrays and more Python Features</h1>
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<h2> Contents </h2>
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<ul class="visible nav section-nav flex-column">
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#introduction">
2.1. Introduction
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<a class="reference internal nav-link" href="#important-matrix-and-vector-handling-packages">
2.2. Important Matrix and vector handling packages
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<a class="reference internal nav-link" href="#basic-matrix-features">
2.3. Basic Matrix Features
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2.3.1. Some famous Matrices
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<a class="reference internal nav-link" href="#numpy-and-arrays">
2.4. Numpy and arrays
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2.5. Other Matrix and Vector Operations
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2.6. Gaussian Elimination
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2.6.1. LU Decomposition, the inverse of a matrix
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@@ -476,8 +544,8 @@ matrices and vectors.</p>
</div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 0.80738685 -0.37307168 -0.28967287 -0.1023111 -0.42394972 -0.04775904
-0.83698677 0.60538875 -0.61463451 -1.12069773]
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0.65444431 -1.35346808 -0.20316225 1.12630042]
</pre></div>
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@@ -698,26 +766,26 @@ as (recall that we user lowercase letters for vectors and uppercase letters for
</div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.40214433 0.46508305 0.10620135 0.26186844 0.28067036 0.092066
0.30552077 0.51265232 0.57673618 0.76674796]
[0.92626212 0.11046771 0.14484695 0.03981057 0.09856879 0.81187794
0.43135183 0.43552433 0.03794112 0.96606158]
[0.76066069 0.84232163 0.38336316 0.53312754 0.35147135 0.05434571
0.21472683 0.96527903 0.18912963 0.56302854]
[0.21786964 0.08428156 0.90895045 0.70205195 0.70980493 0.90884627
0.09085624 0.35892474 0.68246089 0.51561271]
[0.15891336 0.25259666 0.75106135 0.07878641 0.96032148 0.31605061
0.60236938 0.04368707 0.34568872 0.24276315]
[0.98794823 0.88871662 0.16740002 0.21997099 0.18156717 0.11402309
0.85758696 0.51389553 0.45290829 0.89274639]
[0.21519063 0.20174121 0.32320052 0.34585355 0.93579127 0.07735703
0.63860687 0.10302062 0.28047021 0.48212873]
[0.50727059 0.89873772 0.28875373 0.65628853 0.87940752 0.68279358
0.51004249 0.46567887 0.37415316 0.91383439]
[0.90940378 0.25792767 0.17930649 0.24512498 0.10505137 0.0714956
0.69493539 0.35203688 0.1583767 0.80747253]
[0.98266587 0.39456996 0.48574149 0.461175 0.30384239 0.53423784
0.79009329 0.38868469 0.8991514 0.39560937]]
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0.19158446 0.3263505 0.0536097 0.90066122]
[0.34678929 0.66981186 0.44152248 0.20299677 0.1614891 0.68485505
0.43333886 0.45741697 0.31311243 0.88001352]
[0.29661191 0.05268304 0.98153145 0.9007164 0.69481746 0.35319678
0.88063413 0.06319374 0.06695337 0.75350216]
[0.15089627 0.58671946 0.13734823 0.72394787 0.38019139 0.422275
0.35821426 0.49282737 0.19144544 0.84653115]
[0.38637915 0.8049181 0.49672291 0.98699753 0.8192798 0.05850532
0.00152188 0.13131825 0.31229747 0.40183706]
[0.8705211 0.1472032 0.22567203 0.55202922 0.62683307 0.41566661
0.23659936 0.85086629 0.85120833 0.79135075]
[0.31377492 0.38629844 0.33956555 0.64064128 0.42028578 0.58474054
0.71760245 0.51732028 0.31211671 0.35894575]
[0.78286771 0.72594302 0.22821344 0.23962594 0.48739546 0.59190877
0.8557822 0.44830642 0.90595152 0.9626883 ]
[0.34498451 0.90694878 0.15442554 0.43560678 0.89045167 0.21654926
0.00355118 0.18695705 0.61123608 0.7386068 ]
[0.30813073 0.26549135 0.96812218 0.94321297 0.81592628 0.60980325
0.4284066 0.8792323 0.92968793 0.82073684]]
</pre></div>
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@@ -777,13 +845,13 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
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<div class="cell_output docutils container">
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4.098802859381565
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[[0.89550839 2.74368436 2.15717291]
[2.74368436 9.71131626 6.39311435]
[2.15717291 6.39311435 7.55505907]]
[15.92603747 0.07903849 2.15680777]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.2246674023625205
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[26.06969872 0.07319349 2.51150176]
</pre></div>
</div>
</div>
@@ -1333,54 +1401,42 @@ These details will be presented in our linear regression chapter.</p>
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