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":
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  case "ZERO":
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  case "ZEROS":

Revision as of 05:17, 11 January 2018

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 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 (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":
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