Difference between revisions of "Manuals/calci/DIAGONALWITH"

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==Description==
 
==Description==
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*This function gives the matrix satisfying the diagonal properties.  
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* This function gives the matrix satisfying the diagonal properties.  
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*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>).
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* 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>).
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*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.
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*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.
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** Types of Properties:
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*The general diagonal matrix is of the form:
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  case "POSITIVE":
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<math>\begin{bmatrix}
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  case "NEGATIVE":
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c_{1} & 0  & \cdots & 0      \\
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  case "NATURAL":
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0 & c_{2} & \cdots & 0 \\
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  case "POSITIVE:INTEGER":
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\vdots & \vdots &\ddots & \vdots \\
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  case "NEGATIVE:INTEGER":
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0 & 0 & \cdots & c_{n}
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  case "INTEGER":
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\end{bmatrix} </math>
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  case "NEGZEROPOS":
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*So the main diagonal entries are need not to be zero and off-diagonal entries are zero.
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  case "VALUE":
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  case "LIST":
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  case "SERIES":
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  case "SEED":
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  case "FUNCTION":
 +
  case "ZERO":
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  case "ZEROS":

Revision as of 06:17, 11 January 2018

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


  • is any nxn square matrix.


Description

  • This function gives the matrix satisfying 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":
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