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|00000000| 5c 73 65 63 74 69 6f 6e | 7b 61 62 73 20 2d 2d 2d |\section|{abs ---|
|00000010| 20 41 62 73 6f 6c 75 74 | 65 20 56 61 6c 75 65 7d | Absolut|e Value}|
|00000020| 0d 5c 6c 61 62 65 6c 7b | 66 6e 3a 61 62 73 7d 0d |.\label{|fn:abs}.|
|00000030| 5c 69 6e 64 65 78 7b 61 | 62 73 28 29 7d 0d 5c 69 |\index{a|bs()}.\i|
|00000040| 6e 64 65 78 7b 61 62 73 | 6f 6c 75 74 65 20 76 61 |ndex{abs|olute va|
|00000050| 6c 75 65 7d 0d 5c 69 6e | 64 65 78 7b 6d 61 67 6e |lue}.\in|dex{magn|
|00000060| 69 74 75 64 65 7d 0d 5c | 62 65 67 69 6e 7b 72 61 |itude}.\|begin{ra|
|00000070| 69 6c 7d 0d 41 62 73 6f | 6c 75 74 65 56 61 6c 75 |il}.Abso|luteValu|
|00000080| 65 20 3a 20 27 61 62 73 | 27 20 27 28 27 20 28 20 |e : 'abs|' '(' ( |
|00000090| 53 63 61 6c 61 72 20 7c | 20 4d 61 74 72 69 78 20 |Scalar || Matrix |
|000000a0| 29 20 27 29 27 20 3b 0d | 5c 65 6e 64 7b 72 61 69 |) ')' ;.|\end{rai|
|000000b0| 6c 7d 0d 0d 5c 76 65 72 | 62 2b 61 62 73 2b 20 72 |l}..\ver|b+abs+ r|
|000000c0| 65 74 75 72 6e 73 20 74 | 68 65 20 61 62 73 6f 6c |eturns t|he absol|
|000000d0| 75 74 65 20 76 61 6c 75 | 65 20 6f 66 20 74 68 65 |ute valu|e of the|
|000000e0| 20 61 72 67 75 6d 65 6e | 74 2e 20 20 49 74 20 6f | argumen|t.  It o|
|000000f0| 70 65 72 61 74 65 73 0d | 65 6c 65 6d 65 6e 74 2d |perates.|element-|
|00000100| 62 79 2d 65 6c 65 6d 65 | 6e 74 20 66 6f 72 20 61 |by-eleme|nt for a|
|00000110| 20 6d 61 74 72 69 78 20 | 61 72 67 75 6d 65 6e 74 | matrix |argument|
|00000120| 2c 20 72 65 74 75 72 6e | 69 6e 67 20 61 20 6d 61 |, return|ing a ma|
|00000130| 74 72 69 78 20 72 65 73 | 75 6c 74 2e 0d 41 62 73 |trix res|ult..Abs|
|00000140| 6f 6c 75 74 65 20 76 61 | 6c 75 65 20 69 73 20 64 |olute va|lue is d|
|00000150| 65 66 69 6e 65 64 20 61 | 73 20 0d 5c 5b 20 5c 6c |efined a|s .\[ \l|
|00000160| 65 66 74 5c 7b 20 5c 62 | 65 67 69 6e 7b 61 72 72 |eft\{ \b|egin{arr|
|00000170| 61 79 7d 7b 6c 6c 7d 0d | 20 20 20 20 20 20 20 20 |ay}{ll}.|        |
|00000180| 2d 78 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |-x      |        |
|00000190| 26 20 5c 6d 62 6f 78 7b | 69 66 20 24 78 20 3c 20 |& \mbox{|if $x < |
|000001a0| 30 24 20 61 6e 64 20 24 | 78 24 20 69 73 20 72 65 |0$ and $|x$ is re|
|000001b0| 61 6c 7d 20 5c 5c 0d 20 | 20 20 20 20 20 20 20 20 |al} \\. |        |
|000001c0| 78 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 26 |x       |       &|
|000001d0| 20 5c 6d 62 6f 78 7b 69 | 66 20 24 78 20 5c 67 65 | \mbox{i|f $x \ge|
|000001e0| 71 20 30 24 20 61 6e 64 | 20 24 78 24 20 69 73 20 |q 0$ and| $x$ is |
|000001f0| 72 65 61 6c 7d 20 5c 5c | 0d 20 20 20 20 20 20 20 |real} \\|.       |
|00000200| 20 5c 73 71 72 74 7b 5c | 52 65 28 78 29 5e 7b 32 | \sqrt{\|Re(x)^{2|
|00000210| 7d 20 2b 20 5c 49 6d 28 | 78 29 5e 7b 32 7d 7d 20 |} + \Im(|x)^{2}} |
|00000220| 20 20 26 20 5c 6d 62 6f | 78 7b 69 66 20 24 78 24 |  & \mbo|x{if $x$|
|00000230| 20 69 73 20 63 6f 6d 70 | 6c 65 78 7d 0d 20 20 20 | is comp|lex}.   |
|00000240| 20 20 20 20 20 5c 65 6e | 64 7b 61 72 72 61 79 7d |     \en|d{array}|
|00000250| 0d 20 20 20 5c 72 69 67 | 68 74 2e 20 5c 5d 0d 0d |.   \rig|ht. \]..|
|00000260| 0d 5c 70 61 72 61 67 72 | 61 70 68 7b 45 78 61 6d |.\paragr|aph{Exam|
|00000270| 70 6c 65 7d 0d 5c 69 6e | 64 65 78 7b 65 78 61 6d |ple}.\in|dex{exam|
|00000280| 70 6c 65 20 6f 66 20 61 | 62 73 28 29 7d 0d 5c 69 |ple of a|bs()}.\i|
|00000290| 6e 64 65 78 7b 61 62 73 | 28 29 21 65 78 61 6d 70 |ndex{abs|()!examp|
|000002a0| 6c 65 7d 0d 5c 62 65 67 | 69 6e 7b 76 65 72 62 61 |le}.\beg|in{verba|
|000002b0| 74 69 6d 7d 0d 3e 20 61 | 62 73 28 32 2e 33 34 29 |tim}.> a|bs(2.34)|
|000002c0| 0d 20 20 20 20 20 32 2e | 33 34 0d 3e 20 61 62 73 |.     2.|34.> abs|
|000002d0| 28 2d 32 2e 33 34 29 0d | 20 20 20 20 20 32 2e 33 |(-2.34).|     2.3|
|000002e0| 34 0d 3e 20 61 62 73 28 | 2d 32 2e 33 34 20 2b 20 |4.> abs(|-2.34 + |
|000002f0| 34 6a 29 0d 20 20 20 20 | 20 34 2e 36 33 0d 3e 20 |4j).    | 4.63.> |
|00000300| 73 71 72 74 28 28 2d 32 | 2e 33 34 29 5e 32 20 2b |sqrt((-2|.34)^2 +|
|00000310| 20 28 34 29 5e 32 29 0d | 20 20 20 20 20 34 2e 36 | (4)^2).|     4.6|
|00000320| 33 0d 3e 20 62 20 3d 20 | 5b 20 2d 33 2e 34 2c 20 |3.> b = |[ -3.4, |
|00000330| 34 2e 36 30 39 37 3b 20 | 33 2b 34 6a 20 2c 20 2d |4.6097; |3+4j , -|
|00000340| 33 34 2e 35 36 35 33 20 | 2d 30 2e 30 31 6a 5d 0d |34.5653 |-0.01j].|
|00000350| 20 62 20 3d 0d 20 20 20 | 20 20 20 20 20 20 20 20 | b =.   |        |
|00000360| 20 20 20 20 2d 33 2e 34 | 20 2b 20 30 69 20 20 20 |    -3.4| + 0i   |
|00000370| 20 20 20 20 20 20 20 20 | 20 20 20 20 34 2e 36 31 |        |    4.61|
|00000380| 20 2b 20 30 69 0d 20 20 | 20 20 20 20 20 20 20 20 | + 0i.  |        |
|00000390| 20 20 20 20 20 20 20 20 | 33 20 2b 20 34 69 20 20 |        |3 + 4i  |
|000003a0| 20 20 20 20 20 20 20 20 | 20 2d 33 34 2e 36 20 2d |        | -34.6 -|
|000003b0| 20 30 2e 30 31 69 0d 3e | 20 61 62 73 28 62 29 0d | 0.01i.>| abs(b).|
|000003c0| 20 20 20 20 20 20 33 2e | 34 20 20 20 20 20 20 20 |      3.|4       |
|000003d0| 34 2e 36 31 20 20 0d 20 | 20 20 20 20 20 20 20 35 |4.61  . |       5|
|000003e0| 20 20 20 20 20 20 20 33 | 34 2e 36 0d 5c 65 6e 64 |       3|4.6.\end|
|000003f0| 7b 76 65 72 62 61 74 69 | 6d 7d 0d 0d 5c 6e 65 77 |{verbati|m}..\new|
|00000400| 70 61 67 65 0d 0d 0d 0d | 0d 0d                   |page....|..      |
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