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.
+
* 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.
+
* "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}
+
1. DIAGONALWITH([[1,2,3],[4,5,6],[9,8,11]],"NEGATIVE:INTEGER")
−
c_{1} & 0  & \cdots & 0      \\
+
{| class="wikitable"
−
0 & c_{2} & \cdots & 0 \\
+
|-
−
\vdots & \vdots &\ddots & \vdots \\
+
| -18 || 2 || 3
−
0 & 0 & \cdots & c_{n}
+
|-
−
\end{bmatrix} </math>
+
| 4 || -16 || 6
−
*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
 +
|-
 +
| 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]]
 +
*[[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)


  • is any n×n square matrix.
  • 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 ().
  • 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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