Manuals/calci/MATRIXINVERSE - Revision history

Devika: /* Examples */

2019-04-12T19:55:14Z

Examples

Devika at 22:28, 20 June 2017

2017-06-20T22:28:50Z

Devika: /* Description */

2017-06-20T22:19:40Z

Description

Devika: /* Description */

2017-06-20T22:17:13Z

Description

Devika: /* Description */

2017-06-20T22:12:23Z

Description

Devika: /* Description */

2017-06-20T21:55:29Z

Description

Devika: Created page with "
'''MATRIXINVERSE (a)'''

* $a$ is any matrix. ==Description== This function shows the inverse value of the given matrix. In ..."

2017-06-20T21:48:31Z

Created page with "<div style="font-size:30px">'''MATRIXINVERSE (a)'''</div><br/> *<math>a</math> is any matrix. ==Description== *This function shows the inverse value of the given matrix. *In ..."

New page

<div style="font-size:30px">'''MATRIXINVERSE (a)'''</div><br/>
*<math>a</math> is any matrix.

==Description==
*This function shows the inverse value of the given matrix.
*In <math>MATRIXINVERSE (a)</math>, <math>a</math> is any square matrix.
*Inverse of a square matrix is also called reciprocal of a matrix and it is denoted by <math>A^-1</math>.
*Consider the square matrix A has an inverse which should satisfies the following condition <math>|A|\ne 0</math>
*Also <math>AA^{-1}=I</math>(Identity matrix).
*Consider 2x2 matrix:A=[a b;c d].
*The inverse of matrix A is calculated by
<math>A^{-1}={\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}}{-1}</math>,

@@ Line 53: / Line 53: @@
 | -5 || 4 || 1
 |}
 ==See Also==

← Older revision		Revision as of 22:28, 20 June 2017
Line 35:		Line 35:
	\end{bmatrix}}</math>		\end{bmatrix}}</math>
	where A=(ei-fh); B=-(di-fg);C=(dh-eg); D=-(bi-ch); E=(ai-cg); F=-(ah-bg); G=(bf-ce) H=-(af-cd);I=(ae-bd)		where A=(ei-fh); B=-(di-fg);C=(dh-eg); D=-(bi-ch); E=(ai-cg); F=-(ah-bg); G=(bf-ce) H=-(af-cd);I=(ae-bd)
		+
		+	==Examples==
		+	1. MATRIXINVERSE([4,7;2,6])
		+	{\| class="wikitable"
		+	\|-
		+	\| 0.6 \|\| -0.7
		+	\|-
		+	\| -0.2 \|\| 0.4
		+	\|}
		+	2. MATRIXINVERSE([1,2,3;0,1,4;5,6,0])
		+	{\| class="wikitable"
		+	\|-
		+	\| -24 \|\| 18 \|\| 5
		+	\|-
		+	\| 20 \|\| -15 \|\| -4
		+	\|-
		+	\| -5 \|\| 4 \|\| 1
		+	\|}
		+
		+	==See Also==
		+	*[[Manuals/calci/MATRIXOPERATORS\| MATRIXOPERATORS]]
		+	*[[Manuals/calci/MATRIXDETERMINANT\| MATRIXDETERMINANT]]
		+	*[[Manuals/calci/DET\| DET]]
		+
		+	==References==
		+	*[https://en.wikipedia.org/wiki/Invertible_matrix Matrix Inverse]
		+
		+	*[[Z_API_Functions \| List of Main Z Functions]]
		+	*[[ Z3 \| Z3 home ]]

@@ Line 5: / Line 5: @@
 *This function shows the inverse value of the given matrix.
 *In <math>MATRIXINVERSE (a)</math>, <math>a</math> is any square matrix.
-*Inverse of a square matrix is also called reciprocal of a matrix and it is denoted by <math>A^-1</math>.
+*Inverse of a square matrix is also called reciprocal of a matrix and it is denoted by <math>A^{-1}</math>.
 *Consider the square matrix A has an inverse which should satisfies the following condition <math>|A|\ne 0</math>
 *Also <math>AA^{-1}=I</math>(Identity matrix).
@@ Line 16: / Line 16: @@
 d  & -b     \\
 -c  & a
-\end{bmatrix}</math> =\frac{1}{ad-bc} \begin{bmatrix}
+\end{bmatrix}</math> =<math>\frac{1}{ad-bc} \begin{bmatrix}
 d  & -b     \\
 -c  & a

← Older revision		Revision as of 22:17, 20 June 2017
Line 34:		Line 34:
	C & F & I		C & F & I
	\end{bmatrix}}</math>		\end{bmatrix}}</math>
		+	where A=(ei-fh); B=-(di-fg);C=(dh-eg); D=-(bi-ch); E=(ai-cg); F=-(ah-bg); G=(bf-ce) H=-(af-cd);I=(ae-bd)

@@ Line 13: / Line 13: @@
 a  & b     \\
 c  & d
-\end{bmatrix}}^{-1}</math>=<math>1/det A \begin{bmatrix}
+\end{bmatrix}}^{-1}</math>=<math>\frac{1}{det A }\begin{bmatrix}
 d  & -b     \\
 -c  & a
-\end{bmatrix}</math> =<math> 1/ad-bc \begin{bmatrix}
+\end{bmatrix}</math> =\frac{1}{ad-bc} \begin{bmatrix}
 d  & -b     \\
 -c  & a
 \end{bmatrix}</math>

Manuals/calci/MATRIXINVERSE - Revision history

Devika: /* Examples */

Devika at 22:28, 20 June 2017

Devika: /* Description */

Devika: /* Description */

Devika: /* Description */

Devika: /* Description */

Devika: Created page with "'''MATRIXINVERSE (a)''' *a is any matrix. ==Description== *This function shows the inverse value of the given matrix. *In ..."

Devika: Created page with "
'''MATRIXINVERSE (a)'''

* $a$ is any matrix. ==Description== This function shows the inverse value of the given matrix. In ..."