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--- gibson:teaching:spring-2016:math445:lecture:vectors [2016/01/27 09:32]
gibson
+++ gibson:teaching:spring-2016:math445:lecture:vectors [2016/01/28 11:33] (current)
gibson [Math 445 lecture 2: Vectors]
@@ Line 1: / Line 1: @@
 ====== Math 445 lecture 2: Vectors ======
+topics
+<code>
+[]       % creating vector vectors with square brackets
+()       % accessing/assigning vector elements with parentheses
+'        % the transpose operator, apostrophe
+:        % the colon operator, making range vectors
++ -      % vector addition, subtraction
+.* ./ .^ % elementwise vector operations
+</code>
+===== Vectors in math =====
 Vectors are hugely important in math, science, engineering.
@@ Line 17: / Line 28: @@
 </latex>
-In Matlab, there's a distinction between **row vector** and **column vectors**.
+===== Creating vectors with explicit lists in square brackets =====
-You can construct row vectors from explicit lists of elements like this
+In Matlab, there's a distinction between row vector and column vectors.
+You can construct **row vectors** by listing elements between **square brackets**,
+with either **spaces** or **commas** between.
 <code>
-  v = [4.3  5.9  0.1]  % spaces between elements, or
+>> v = [4.3 5.9 0.1]  % assign a row vector into variable v
-  v = [4.3, 5.9, 0.1]  % commas between elements
+v =
+.3000    5.9000    0.1000
 </code>
-You can create column vectors like this
+To create a column vectors, put semicolons between the elements.
 <code>
-  v = [4.3; 5.9; 0.1]  % semicolons between elements, or
+ >> v = [4.3; 5.9; 0.1] % assign a col vector into variable v
-  v = [4.3  5.9  0.1]' % the transpose of a row vector
+v =
+.3000
+.9000
+.1000
 </code>
+===== Accessing elements with parentheses =====
+In Matlab, you access the elements of a vector using **parentheses**. E.g. given the above vector v, you **get** the 2nd component of v this way
+<code>
+>> v(2)
+ans =
+.9000
+</code>
+Note what happened there. We asked Matlab for the 2nd element of v. It **returned** the value 5.9 and assigned it to the default return variable ''ans''. Alternatively, the following will **assign** or **set** the value of the second component of v to another number.
+<code>
+>> v(2) = 2.7
+v =
+.3000
+.7000
+.1000
+</code>
+===== The transpose operator ' (apostrophe) =====
 Note that last method. In Matlab, the apostrophe '' ' '' stands for the **transpose**.
@@ Line 70: / Line 120: @@
 </code>
+===== Constructing vectors with the colon operator : =====
+The Matlab **colon** operator : is used in a number of ways. Here we'll see how it can be used to create vectors. The most straightforward of these is the syntax ''m:n'', which creates a row vector of the integers from ''m'' to ''n''. E.g.
+<code>
+>> 1:10
+ans =
+     2     3     4     5     6     7     8     9    10
+>> x = 4:7
+x =
+     5     6     7
+</code>
+You can also specify a **step** or **increment** between the elements using the syntax ''m:step:n''. For example, ''5:2:17'' will produce a vector of odd integers between 5 and 17.
+<code>
+>> x = 5:2:17
+x =
+     7     9    11    13    15    17
+</code>
+Lastly, the colon operator works with nonintegers, too. E.g.
+<code>
+>> x = 0:0.1:0.7
+x =
+    0.1000    0.2000    0.3000    0.4000    0.5000    0.6000    0.7000
+</code>
+===== Supplemental material =====
+[[https://www.youtube.com/watch?v=zXP_pr7np-o | ' (apostrophe), Frank Zappa (the song)]]
+[[https://www.youtube.com/watch?v=kQDp2425WQ0&list=PL8WvZFiJpAr29HFJkRcE4NvWCeYy3ytte | ' (apostrophe), Frank Zappa (full album) ]]

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