Manuals/calci/VECTORDIRECTPRODUCT - Revision history

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2019-02-07T20:02:39Z

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Examples

Devika at 19:48, 17 May 2017

2017-05-17T19:48:24Z

Devika: Created page with "
'''VECTORDIRECTPRODUCT (a,b)'''

* $a$ and $b$ any two set of values. ==Description== *This function shows the Vec..."

2017-05-17T19:43:01Z

Created page with "<div style="font-size:30px">'''VECTORDIRECTPRODUCT (a,b)'''</div><br/> *<math> a</math> and <math>b</math> any two set of values. ==Description== *This function shows the Vec..."

New page

<div style="font-size:30px">'''VECTORDIRECTPRODUCT (a,b)'''</div><br/>
*<math> a</math> and <math>b</math> any two set of values.

==Description==
*This function shows the Vector Direct product.
*The third type of vector multiplication is called the direct product, and is written AB.
*In <math>VECTORDIRECTPRODUCT (a,b)</math>, <math>a</math> and <math>b</math> are the two vectors.
*Multiplying one vector by another under the direct product gives a tensor result.
*The rectangular components of the direct product may be found by matrix multiplication: one multiplies the column vector A by the transpose of B, which gives a 3X3 matrix:
<math>AB=AB^T</math>=
<math>\begin{pmatrix}
A_x \\
A_y \\
A_z
\end{pmatrix}</math><math> (B_x B_y B_Z)</math>=<math>\begin{pmatrix}
A_xB_x & A_xB_y & A_xB_z \\
A_yB_x & A_yB_y & A_yB_z \\
A_z B_x &A_zB_y & A_zB_z
\end{pmatrix}</math>
*The direct product is non-commutative <math>(AB \neq BA)</math>.
*A few vector product identities are of interest:
#<math>A.BXC = AXB.C=B.CXA=BXC.A=C.AXB</math>
#<math>AX(BXC)= B.(A.C)- C(A.B)</math>
#<math>(AXB)XC = B(A.C)-A(B.C)</math>
#<math>(AXB).(CXD)= (A.C)(B.D)-(A.D)(B.C)</math>
#<math>(AXB).(CXD) = (AxB.D)C-(AxB.C)D</math>

@@ Line 33: / Line 33: @@
 ==Related Videos==
-{{#ev:youtube|v=tpL95Sd7zT0&t=81s|280|center|Equality}}
+{{#ev:youtube|v=tpL95Sd7zT0&t=81s|280|center|Tensor Product}}
 ==See Also==

@@ Line 30: / Line 30: @@
 #VECTORDIRECTPRODUCT([4,-3,5],[3.3,4.2,6]) = 30.599999999999998
 #VECTORDIRECTPRODUCT([2,1,-3],[7,4,-9]) = 45
 ==See Also==

← Older revision		Revision as of 19:48, 17 May 2017
Line 25:		Line 25:
	#<math>(AXB).(CXD)= (A.C)(B.D)-(A.D)(B.C)</math>		#<math>(AXB).(CXD)= (A.C)(B.D)-(A.D)(B.C)</math>
	#<math>(AXB).(CXD) = (AxB.D)C-(AxB.C)D</math>		#<math>(AXB).(CXD) = (AxB.D)C-(AxB.C)D</math>
		+
		+	==Examples==
		+	#VECTORDIRECTPRODUCT([1,2,3],[5,2,9]) = 36
		+	#VECTORDIRECTPRODUCT([4,-3,5],[3.3,4.2,6]) = 30.599999999999998
		+	#VECTORDIRECTPRODUCT([2,1,-3],[7,4,-9]) = 45
		+
		+	==See Also==
		+	*[[Manuals/calci/DOTPRODUCT \| DOTPRODUCT ]]
		+	*[[Manuals/calci/CROSSPRODUCT \| CROSSPRODUCT ]]
		+	*[[Manuals/calci/CARTESIANPRODUCT \| CARTESIANPRODUCT ]]
		+
		+	==References==
		+	[http://www.pgccphy.net/ref/vprod.pdf Direct Product]
		+
		+
		+	*[[Z_API_Functions \| List of Main Z Functions]]
		+	*[[ Z3 \| Z3 home ]]

Manuals/calci/VECTORDIRECTPRODUCT - Revision history

Devika: /* Related Videos */

Devika: /* Examples */

Devika at 19:48, 17 May 2017

Devika: Created page with "'''VECTORDIRECTPRODUCT (a,b)''' * a and b any two set of values. ==Description== *This function shows the Vec..."

Devika: Created page with "
'''VECTORDIRECTPRODUCT (a,b)'''

* $a$ and $b$ any two set of values. ==Description== *This function shows the Vec..."