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Difference between revisions of "Manuals/calci/DIAGONALWITH"
 
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<div style="font-size:30px">'''DIAGONALWITH(Matrix,Properties,Seed,Offset,FillTypeAntiColumnOrRow)'''</div><br/>
 
<div style="font-size:30px">'''DIAGONALWITH(Matrix,Properties,Seed,Offset,FillTypeAntiColumnOrRow)'''</div><br/>
−
*<math>Matrix</math> is any nxn square matrix.
+
*<math>Matrix</math> is any n×n square matrix.
 +
*<math>Properties</math> is any property with which the main diagonal is filled.
  
  
 
==Description==
 
==Description==
−
*This function gives the matrix satisfying the diagonal properties.  
+
* This function gives a matrix which satisfies the diagonal properties.  
−
*An diagonal matrix is a matrix where all the entries are zero on the main diagonal going from the upper left corner to the lower right corner (<math>\searrow</math>).
+
* An diagonal matrix is a matrix where all the entries are zero on the main diagonal going from the upper left corner to the lower right corner (<math>\searrow</math>).
−
*In Diagonalwith, all the elements on main diagonal are filled with the given Properties rather than by 0.
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* In DIAGONALWITH, all the elements on main diagonal are filled with the given Properties rather than by 0.
−
*A diagonal matrix is a square matrix which is of the form <math>a_{ij}=c_{i} \delta_{ij}</math> where <math>\delta_{ij}</math> is the Kronecker delta, <math>c_{i}</math> are constants, and i,j=1, 2, ..., n.
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* "ZERO" is a default Property.
 +
  '''Types of Properties:'''
 +
  case "POSITIVE":
 +
  case "NEGATIVE":
 +
  case "NATURAL":
 +
  case "POSITIVE:INTEGER":
 +
  case "NEGATIVE:INTEGER":
 +
  case "INTEGER":
 +
  case "NEGZEROPOS":
 +
  case "VALUE":
 +
  case "LIST":
 +
  case "SERIES":
 +
  case "SEED":
 +
  case "FUNCTION":
 +
  case "ZERO":
 +
  case "ZEROS":
  
−
*The general diagonal matrix is of the form:
+
==Examples==
−
<math>\begin{bmatrix}
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1. DIAGONALWITH([[1,2,3],[4,5,6],[9,8,11]],"NEGATIVE:INTEGER")
−
c_{1} & 0  & \cdots & 0      \\
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{| class="wikitable"
−
0 & c_{2} & \cdots & 0 \\
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|-
−
\vdots & \vdots &\ddots & \vdots \\
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| -18 || 2 || 3
−
0 & 0 & \cdots & c_{n}
+
|-
−
\end{bmatrix} </math>
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| 4 || -16 || 6
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*So the main diagonal entries are need not to be zero and off-diagonal entries are zero.
+
|-
 +
| 9 || 8 || -64
 +
|}
 +
2. DIAGONALWITH([[11,18,19,20],[78,12,15,23],[-23,-20,-15,65],[5,8,9.2,12.7]],"SERIES")
 +
{| class="wikitable"
 +
|-
 +
| 100 || 18 || 19 || 20
 +
|-
 +
| 78 || 100 || 15 || 23
 +
|-
 +
| -23 || -20 || 100 || 65
 +
|-
 +
| 5 || 8 || 9.2 ||100
 +
|}
 +
3. DIAGONALWITH([[-1,6,8,9],[7,6,12,-98],[11,15,17.2,19]],"LIST")
 +
{| class="wikitable"
 +
|-
 +
| 100 || 6 || 8 || 9
 +
|-
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| 7 || 100 || 12 || -98
 +
|-
 +
| 11 || 15 || 100 || 19
 +
|}
 +
 
 +
==Related Videos==
 +
 
 +
{{#ev:youtube|v=Wc9DwLLXP8k|280|center|Diagonal Matrix}}
 +
 
 +
==See Also==
 +
*[[Manuals/calci/ANTIDIAGONAL | ANTIDIAGONAL]]
 +
*[[Manuals/calci/ARROWHEAD| ARROWHEAD]]
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*[[Manuals/calci/MATRIXOPERATORS| MATRIXOPERATORS]]
 +
 
 +
==References==
 +
*[http://en.wikipedia.org/wiki/Anti-diagonal_matrix Anti Diagonal]
 +
 
 +
 
 +
 
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
 
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 12:44, 9 April 2019

DIAGONALWITH(Matrix,Properties,Seed,Offset,FillTypeAntiColumnOrRow)


  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Matrix} is any n×n square matrix.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Properties} is any property with which the main diagonal is filled.


Description

  • This function gives a matrix which satisfies the diagonal properties.
  • An diagonal matrix is a matrix where all the entries are zero on the main diagonal going from the upper left corner to the lower right corner (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \searrow} ).
  • In DIAGONALWITH, all the elements on main diagonal are filled with the given Properties rather than by 0.
  • "ZERO" is a default Property.
 Types of Properties:
  case "POSITIVE":
  case "NEGATIVE":
  case "NATURAL":
  case "POSITIVE:INTEGER":
  case "NEGATIVE:INTEGER":
  case "INTEGER":
  case "NEGZEROPOS":
  case "VALUE":
  case "LIST":
  case "SERIES":
  case "SEED":
  case "FUNCTION":
  case "ZERO":
  case "ZEROS":

Examples

1. DIAGONALWITH([[1,2,3],[4,5,6],[9,8,11]],"NEGATIVE:INTEGER")

-18 2 3
4 -16 6
9 8 -64

2. DIAGONALWITH([[11,18,19,20],[78,12,15,23],[-23,-20,-15,65],[5,8,9.2,12.7]],"SERIES")

100 18 19 20
78 100 15 23
-23 -20 100 65
5 8 9.2 100

3. DIAGONALWITH([[-1,6,8,9],[7,6,12,-98],[11,15,17.2,19]],"LIST")

100 6 8 9
7 100 12 -98
11 15 100 19

Related Videos

Diagonal Matrix

See Also

References


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