Slides for review of basic concepts in vector calculus and ... - Classes
Slides for review of basic concepts in vector calculus and ... - Classes
Slides for review of basic concepts in vector calculus and ... - Classes
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Review <strong>of</strong> L<strong>in</strong>ear Algebra <strong>and</strong><br />
Vector Calculus<br />
Adopted from notes by Andrew<br />
Rosenberg <strong>of</strong> CUNY
L<strong>in</strong>ear Algebra Basics<br />
• What is a <strong>vector</strong>?<br />
• What is a matrix?<br />
• Transposition<br />
• Add<strong>in</strong>g matrices <strong>and</strong> <strong>vector</strong>s<br />
• Multiply<strong>in</strong>g matrices.
Def<strong>in</strong>itions<br />
• A <strong>vector</strong> is a one dimensional array.<br />
• We denote <strong>vector</strong>s as boldface lower case<br />
letter x<br />
• If we don’t specify otherwise assume x is a<br />
column <strong>vector</strong>
Def<strong>in</strong>ition
Transposition
Inner Product (AKA Dot product)<br />
• The <strong>in</strong>ner product <strong>of</strong> two equal‐length <strong>vector</strong>s<br />
x <strong>and</strong> y is def<strong>in</strong>ed as:<br />
= x T y= (x 0 y 0 +x 1 y 1 +….+x n‐1 y n‐1 )
Useful matrix operations<br />
• Inversion<br />
• Norm<br />
• Eigen<strong>vector</strong> decomposition
Matrix Inversion
Some useful Matrix Inversion<br />
Properties
The norm <strong>of</strong> a <strong>vector</strong>
Eigen<strong>vector</strong>s
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