Difference between revisions of "Manuals/calci/MINVERSE"

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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> '''MINVERSE'''(Array) where, '''Array''' -  represents array having equal number of rows and columns. </di...")
 
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<div style="font-size:30px">'''MINVERSE(arr)'''</div><br/>
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*<math>arr</math> is the  array of numeric elements
  
'''MINVERSE'''(Array)
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==Description==
 +
*This function gives the inverse matrix for the given matrix.
 +
*We have to find a inverse of a matrix then it should satisfy the following conditions
 +
*1.A matrix must be a square matrix.
 +
*2.It's determinant not equal to 0.
 +
*Let <math>A<math> be the 2x2 matrix with the elements A=|a    b
 +
                                                          c    d|.
 +
*Then the inverse of matrix <math>A<math> is denoted by A^-1.So A^-1=|a        b|^-=1/ad-bc  |d    -b
 +
                                                                                  -c    a|.
 +
*Now let A be the matrix is of order nXn.
 +
*Then the inverse of A is A^-1= 1/det(A) . adj(A)
 +
*Where adj(A) is the adjoint of A.
 +
*Adjoint is the matrix formed by taking the transpose of the co-factor matrix of a given original matrix.
 +
*Also A.A^-1=A^-1.A=I, where I is the identity matrix.Non-square matrices do not have inverses.
 +
*Not all square matrices have inverses.
 +
*A square matrix which has an inverse is called invertible or non-singular, and a square matrix without an inverse is called non-invertible or singular.
 +
*This function will return the result as error when
 +
1. Any one of the cell is non-numeric or any cell is empty or contain text
 +
2. Suppose number of rows not equal to number of columns
  
where,
 
  
'''Array''' -  represents array having equal number of rows and columns.
+
== Examples ==
 +
Matrix A
 +
A=(4    3
 +
  3    2)
 +
MINVERSE(B5:C6)=(-2      3
 +
                  3      -4)
 +
MATRIX A
 +
A=(3      4
 +
      6      8)
 +
MINVERSE(C4:D5)=Null, because its det value is 0.
 +
MATRIX A
 +
A=(2    3
 +
  4    7)
 +
MINVERSE(B4:C5)=(3.5      -1.5
 +
                -2          1)
  
</div>
 
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<div id="1SpaceContent" class="zcontent" align="left">
 
  
It returns the inverse matrix having equal number of rows and columns based on given array.
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==See Also==
  
</div>
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*[[Manuals/calci/COS | COS]]
----
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*[[Manuals/calci/TAN | TAN]]
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*[[Manuals/calci/ASIN| ASIN]]
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*[[Manuals/calci/DSIN | DSIN]]
  
If Array have different number of rows and column, MINVERSE returns the #ERROR.
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==References==
  
</div>
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*[http://en.wikipedia.org/wiki/Trigonometric_functions List of Trigonometric Functions]
----
+
*[http://en.wikipedia.org/wiki/Sine SIN]
<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
 
 
 
MINVERSE
 
 
 
</div></div>
 
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Lets see an example in (Column2, Row5)
 
 
 
<nowiki>=MINVERSE(R1C1:R2C2)</nowiki>
 
 
 
MINVERSE returns array[-1.5,1.25,0.5,-0.25].
 
 
 
</div>
 
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<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div>
 
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<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
 
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<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
 
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<div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
 
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{| id="TABLE3" class="SpreadSheet blue"
 
|- class="even"
 
| class=" " |
 
| class="  " | Column1
 
| Column2
 
| Column3
 
| Column4
 
|- class="odd"
 
| class=" " | Row1
 
| class="                                                  " | 1
 
| class=" " | 5
 
|
 
|
 
|- class="even"
 
| class="  " | Row2
 
| class=" " | 2
 
| class=" " | 6
 
|
 
|
 
|- class="odd"
 
| Row3
 
| class="sshl_f" | -1.5,1.25,0.5,-0.25
 
|
 
|
 
|
 
|- class="even"
 
| Row4
 
| class=" SelectTD ChangeBGColor SelectTD" |
 
|
 
|
 
|
 
|- class="odd"
 
| class=" " | Row5
 
|
 
|
 
|
 
|
 
|- class="even"
 
| Row6
 
|
 
| class="  " |
 
|
 
|
 
|}
 
 
 
<div align="left">[[Image:calci1.gif]]</div></div>
 
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Revision as of 04:44, 1 January 2014

MINVERSE(arr)


  • is the array of numeric elements

Description

  • This function gives the inverse matrix for the given matrix.
  • We have to find a inverse of a matrix then it should satisfy the following conditions
  • 1.A matrix must be a square matrix.
  • 2.It's determinant not equal to 0.
  • Let <math>A<math> be the 2x2 matrix with the elements A=|a b
                                                         c     d|.
  • Then the inverse of matrix <math>A<math> is denoted by A^-1.So A^-1=|a b|^-=1/ad-bc |d -b
                                                                                 -c     a|.
  • Now let A be the matrix is of order nXn.
  • Then the inverse of A is A^-1= 1/det(A) . adj(A)
  • Where adj(A) is the adjoint of A.
  • Adjoint is the matrix formed by taking the transpose of the co-factor matrix of a given original matrix.
  • Also A.A^-1=A^-1.A=I, where I is the identity matrix.Non-square matrices do not have inverses.
  • Not all square matrices have inverses.
  • A square matrix which has an inverse is called invertible or non-singular, and a square matrix without an inverse is called non-invertible or singular.
  • This function will return the result as error when
1. Any one of the cell is non-numeric or any cell is empty or contain text
2. Suppose number of rows not equal to number of columns


Examples

Matrix A A=(4 3

  3     2)

MINVERSE(B5:C6)=(-2 3

                 3       -4)

MATRIX A A=(3 4

     6       8)

MINVERSE(C4:D5)=Null, because its det value is 0. MATRIX A A=(2 3

  4     7)

MINVERSE(B4:C5)=(3.5 -1.5

               -2           1)


See Also

References