Difference between revisions of "Manuals/calci/BIDIAGONAL"

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<div style="font-size:30px">'''BIDIAGONAL'''</div><br/>
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<div style="font-size:30px">'''MATRIX("BIDIAGONAL",order)'''</div><br/>
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*<math>order</math> is the size of the Bidiagonal matrix.
 +
 
 +
==Description==
 +
*This function returns the matrix with the property of bidiagonal.
 +
*A bidiagonal matrix has non zero entries only on the main bidiagonal and either the first super-diagonal and first sub-diagonal.
 +
*In Calci,users will get different types of bidiagonal matrices.
 +
*There are two types are there lower bidiagonal and upper bidiagonal.
 +
*When the diagonal below the main diagonal has the non-zero entries the matrix is lower bidiagonal.
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*When the diagonal above the main diagonal has the non-zero entries the matrix is upper bidiagonal.
 +
*The example of lower bidiagonal matrix is:
 +
<math>A=\begin{pmatrix}
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62 & 0 & 0 & 0 \\
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-60 & 69 & 0 & 0 \\
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0 & -52 & 65 & 0 \\
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0 & 0 & -18 & 1 \\
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\end{pmatrix} </math>
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*The example of a upper bidiagonal matrix is:
 +
<math>A=\begin{pmatrix}
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56 & 18 & 0 & 0 \\
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0 & -33 & -55 & 0 \\
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0 & 0 & -2 & -60 \\
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0 & 0 & 0 & -9 \\
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\end{pmatrix} </math>
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*The syntax of lower and upper bidiagonal matrices are MATRIX("lowerbidiagonal") or MATRIX("lower-bidiagonal") and MATRIX("upperbidiagonal") or MATRIX("upper-bidiagonal")
 +
 
 +
==Examples==
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*1.MATRIX("bidiagonal") = 70
 +
*2.MATRIX("bidiagonal",3)
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{| class="wikitable"
 +
|-
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| -63 || 97 || 0
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|-
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| 0 || 44 || 65
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|-
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| 0 || 0 || 97
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|}
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*3.MATRIX("bidiagonal",5)
 +
{| class="wikitable"
 +
|-
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| 77 || -7 || 0 || 0 || 0
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|-
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| 0 || 83 || 56 || 0 || 0
 +
|-
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| 0 || 0 || 2 || -88 || 0
 +
|-
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| 0 || 0 || 0 || -88 || -59
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|-
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| 0 || 0 || 0 || 0 || 87
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|}
 +
*4.MATRIX("upper-bidiagonal",3)
 +
{| class="wikitable"
 +
|-
 +
| -5 || 40 || 0
 +
|-
 +
| 0 || 5 || 71 
 +
|-
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| 0 || 0 || 19
 +
|}
 +
*5.MATRIX("lowerbidiagonal",4)
 +
{| class="wikitable"
 +
|-
 +
| 87 || 0 || 0 || 0
 +
|-
 +
| 8 || -13 || 0 || 0 
 +
|-
 +
| 0 || -70 || 82 || 0
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|-
 +
| 0 || 0 || 94 || -33
 +
|}
 +
 
 +
==Related Videos==
 +
 
 +
{{#ev:youtube|F9wVeCg03rA|280|center|Banded Matrix, Tri-diagonal Matrix}}
 +
 
 +
==See Also==
 +
*[[Manuals/calci/PERSYMMETRIC| PERSYMMETRIC]]
 +
*[[Manuals/calci/PASCAL| PASCAL]]
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*[[Manuals/calci/TRIANGULAR| TRIANGULAR]]
 +
 
 +
==References==
 +
*[http://en.wikipedia.org/wiki/Bidiagonal_matrix Bidiagonal]

Latest revision as of 00:27, 26 October 2015

MATRIX("BIDIAGONAL",order)


  • is the size of the Bidiagonal matrix.

Description

  • This function returns the matrix with the property of bidiagonal.
  • A bidiagonal matrix has non zero entries only on the main bidiagonal and either the first super-diagonal and first sub-diagonal.
  • In Calci,users will get different types of bidiagonal matrices.
  • There are two types are there lower bidiagonal and upper bidiagonal.
  • When the diagonal below the main diagonal has the non-zero entries the matrix is lower bidiagonal.
  • When the diagonal above the main diagonal has the non-zero entries the matrix is upper bidiagonal.
  • The example of lower bidiagonal matrix is:

  • The example of a upper bidiagonal matrix is:

  • The syntax of lower and upper bidiagonal matrices are MATRIX("lowerbidiagonal") or MATRIX("lower-bidiagonal") and MATRIX("upperbidiagonal") or MATRIX("upper-bidiagonal")

Examples

  • 1.MATRIX("bidiagonal") = 70
  • 2.MATRIX("bidiagonal",3)
-63 97 0
0 44 65
0 0 97
  • 3.MATRIX("bidiagonal",5)
77 -7 0 0 0
0 83 56 0 0
0 0 2 -88 0
0 0 0 -88 -59
0 0 0 0 87
  • 4.MATRIX("upper-bidiagonal",3)
-5 40 0
0 5 71
0 0 19
  • 5.MATRIX("lowerbidiagonal",4)
87 0 0 0
8 -13 0 0
0 -70 82 0
0 0 94 -33

Related Videos

Banded Matrix, Tri-diagonal Matrix

See Also

References

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