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|00000000| 5c 73 65 63 74 69 6f 6e | 7b 64 69 61 67 20 2d 2d |\section|{diag --|
|00000010| 2d 20 44 69 61 67 6f 6e | 61 6c 69 73 65 20 6d 61 |- Diagon|alise ma|
|00000020| 74 72 69 78 7d 0d 5c 6c | 61 62 65 6c 7b 66 6e 3a |trix}.\l|abel{fn:|
|00000030| 64 69 61 67 7d 0d 5c 69 | 6e 64 65 78 7b 64 69 61 |diag}.\i|ndex{dia|
|00000040| 67 28 29 7d 0d 5c 69 6e | 64 65 78 7b 64 69 61 67 |g()}.\in|dex{diag|
|00000050| 6f 6e 61 6c 69 73 65 20 | 6d 61 74 72 69 78 7d 0d |onalise |matrix}.|
|00000060| 5c 69 6e 64 65 78 7b 6d | 61 74 72 69 78 21 64 69 |\index{m|atrix!di|
|00000070| 61 67 6f 6e 61 6c 7d 0d | 5c 62 65 67 69 6e 7b 72 |agonal}.|\begin{r|
|00000080| 61 69 6c 7d 0d 44 69 61 | 67 6f 6e 61 6c 69 73 65 |ail}.Dia|gonalise|
|00000090| 20 3a 20 27 64 69 61 67 | 27 20 27 28 27 20 4d 61 | : 'diag|' '(' Ma|
|000000a0| 74 72 69 78 20 28 20 28 | 29 20 7c 20 28 20 27 2c |trix ( (|) | ( ',|
|000000b0| 27 20 53 63 61 6c 61 72 | 20 29 20 29 20 20 27 29 |' Scalar| ) )  ')|
|000000c0| 27 20 3b 0d 5c 65 6e 64 | 7b 72 61 69 6c 7d 0d 0d |' ;.\end|{rail}..|
|000000d0| 5c 76 65 72 62 2b 64 69 | 61 67 2b 20 68 61 73 20 |\verb+di|ag+ has |
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|00000160| 64 69 61 67 2b 20 72 65 | 74 75 72 6e 73 20 61 20 |diag+ re|turns a |
|00000170| 73 71 75 61 72 65 20 6d | 61 74 72 69 78 20 77 69 |square m|atrix wi|
|00000180| 74 68 20 74 68 61 74 20 | 76 65 63 74 6f 72 20 6f |th that |vector o|
|00000190| 6e 20 61 20 64 69 61 67 | 6f 6e 61 6c 2e 0d 0d 57 |n a diag|onal...W|
|000001a0| 68 69 63 68 20 64 69 61 | 67 6f 6e 61 6c 20 74 68 |hich dia|gonal th|
|000001b0| 65 20 76 65 63 74 6f 72 | 20 69 73 20 70 6c 61 63 |e vector| is plac|
|000001c0| 65 64 20 6f 6e 20 69 73 | 20 64 65 74 65 72 6d 69 |ed on is| determi|
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|000001f0| 68 20 64 65 66 61 75 6c | 74 73 20 74 6f 20 24 30 |h defaul|ts to $0|
|00000200| 24 20 69 66 20 79 6f 75 | 20 64 6f 6e 27 74 20 73 |$ if you| don't s|
|00000210| 70 65 63 69 66 79 20 69 | 74 2e 20 20 54 68 65 20 |pecify i|t.  The |
|00000220| 6d 61 69 6e 0d 64 69 61 | 67 6f 6e 61 6c 20 69 73 |main.dia|gonal is|
|00000230| 20 74 61 6b 65 6e 20 61 | 73 20 24 30 24 2e 20 20 | taken a|s $0$.  |
|00000240| 54 68 65 20 64 69 61 67 | 6f 6e 61 6c 20 61 62 6f |The diag|onal abo|
|00000250| 76 65 20 74 68 65 20 6d | 61 69 6e 20 64 69 61 67 |ve the m|ain diag|
|00000260| 6f 6e 61 6c 20 61 72 65 | 0d 74 61 6b 65 6e 20 61 |onal are|.taken a|
|00000270| 73 20 70 6f 73 69 74 69 | 76 65 20 69 6e 74 65 67 |s positi|ve integ|
|00000280| 65 72 73 2c 20 61 6e 64 | 20 74 68 65 20 64 69 61 |ers, and| the dia|
|00000290| 67 6f 6e 61 6c 73 20 62 | 65 6c 6f 77 20 74 68 65 |gonals b|elow the|
|000002a0| 20 6d 61 69 6e 20 64 69 | 61 67 6f 6e 61 6c 0d 61 | main di|agonal.a|
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|000002d0| 64 20 66 6f 72 6d 20 6f | 66 20 5c 76 65 72 62 2b |d form o|f \verb+|
|000002e0| 64 69 61 67 2b 20 69 73 | 20 75 73 65 64 20 69 66 |diag+ is| used if|
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|00000310| 20 6f 72 20 63 6f 6c 75 | 6d 6e 20 76 65 63 74 6f | or colu|mn vecto|
|00000320| 72 2e 20 20 54 68 65 20 | 72 65 73 75 6c 74 20 6f |r.  The |result o|
|00000330| 66 20 74 68 69 73 20 6f | 70 65 72 61 74 69 6f 6e |f this o|peration|
|00000340| 20 69 73 20 61 20 63 6f | 6c 75 6d 6e 20 6d 61 74 | is a co|lumn mat|
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|00000360| 66 20 61 6c 6c 20 74 68 | 65 20 65 6c 65 6d 65 6e |f all th|e elemen|
|00000370| 74 73 20 74 61 6b 65 6e | 20 66 72 6f 6d 20 61 20 |ts taken| from a |
|00000380| 64 69 61 67 6f 6e 61 6c | 2e 20 20 41 73 20 66 6f |diagonal|.  As fo|
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|000003e0| 6f 6e 61 6c 20 74 6f 20 | 65 78 74 72 61 63 74 20 |onal to |extract |
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|00000460| 73 70 65 63 69 66 79 20 | 61 20 6d 61 74 72 69 78 |specify |a matrix|
|00000470| 20 61 73 20 74 68 65 20 | 73 65 63 6f 6e 64 0d 61 | as the |second.a|
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|00000490| 20 75 73 65 73 20 74 68 | 65 20 66 69 72 73 74 20 | uses th|e first |
|000004a0| 65 6c 65 6d 65 6e 74 20 | 6f 66 20 74 68 61 74 20 |element |of that |
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|000004c0| 69 6e 65 0d 74 68 65 20 | 64 69 61 67 6f 6e 61 6c |ine.the |diagonal|
|000004d0| 20 74 6f 20 75 73 65 2e | 0d 0d 0d 5c 70 61 72 61 | to use.|...\para|
|000004e0| 67 72 61 70 68 7b 45 78 | 61 6d 70 6c 65 7d 0d 5c |graph{Ex|ample}.\|
|000004f0| 69 6e 64 65 78 7b 65 78 | 61 6d 70 6c 65 20 6f 66 |index{ex|ample of|
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|00000520| 5c 62 65 67 69 6e 7b 76 | 65 72 62 61 74 69 6d 7d |\begin{v|erbatim}|
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|000005f0| 64 69 61 67 28 61 29 0d | 20 20 20 20 20 20 20 20 |diag(a).|        |
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|00000670| 0d 3e 20 64 69 61 67 28 | 61 2c 32 29 0d 20 20 20 |.> diag(|a,2).   |
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|000006a0| 0d 3e 20 62 20 3d 20 31 | 3a 33 0d 20 62 20 3d 0d |.> b = 1|:3. b =.|
|000006b0| 20 20 20 20 20 20 20 20 | 31 20 20 20 20 20 20 20 |        |1       |
|000006c0| 20 20 20 32 20 20 20 20 | 20 20 20 20 20 20 33 20 |   2    |      3 |
|000006d0| 20 0d 3e 20 64 69 61 67 | 28 62 29 0d 20 20 20 20 | .> diag|(b).    |
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|00000730| 20 20 20 30 20 20 20 20 | 20 20 20 20 20 20 33 20 |   0    |      3 |
|00000740| 20 0d 3e 20 64 69 61 67 | 28 62 2c 31 29 0d 20 20 | .> diag|(b,1).  |
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|000007e0| 20 20 20 20 20 20 20 20 | 30 20 20 20 20 20 20 20 |        |0       |
|000007f0| 20 20 20 30 20 20 20 20 | 20 20 20 20 20 20 30 20 |   0    |      0 |
|00000800| 20 0d 5c 65 6e 64 7b 76 | 65 72 62 61 74 69 6d 7d | .\end{v|erbatim}|
|00000810| 0d 0d 53 65 65 20 61 6c | 73 6f 3a 20 50 61 67 65 |..See al|so: Page|
|00000820| 7e 5c 70 61 67 65 72 65 | 66 7b 66 6e 3a 74 72 69 |~\pagere|f{fn:tri|
|00000830| 6c 7d 20 5c 76 65 72 62 | 2b 74 72 69 6c 28 29 2b |l} \verb|+tril()+|
|00000840| 2c 0d 50 61 67 65 7e 5c | 70 61 67 65 72 65 66 7b |,.Page~\|pageref{|
|00000850| 66 6e 3a 74 72 69 75 7d | 20 5c 76 65 72 62 2b 74 |fn:triu}| \verb+t|
|00000860| 72 69 75 28 29 2b 2e 0d | 0d 5c 6e 65 77 70 61 67 |riu()+..|.\newpag|
|00000870| 65 0d 0d 0d 0d 0d 0d    |                         |e...... |        |
+--------+-------------------------+-------------------------+--------+--------+