Matrix - Revision history

WikiSysop at 04:27, 3 June 2022

2022-06-03T04:27:12Z

← Older revision		Revision as of 00:27, 3 June 2022
Line 97:		Line 97:
	0.11229 0.32361		0.11229 0.32361
	<9○1⌷[2]!⌻∘⌻c ⍝ Complex number whose coefficients are ...		<9○1⌷[2]!⌻∘⌻c ⍝ Complex number whose coefficients are ...
	0.~~11229J0~~.32361		0.11229<_J/>0.32361
	!c ⍝ Using a different algorithm (GSL Complex factorial)		!c ⍝ Using a different algorithm (GSL Complex factorial)
	0.~~11229J0~~.32361		0.11229<_J/>0.32361

	⍝ Factorial of a Quaternion		⍝ Factorial of a Quaternion
Line 118:		Line 118:
	0.0060975 ¯0.0010787 ¯0.001618 ¯0.0021573		0.0060975 ¯0.0010787 ¯0.001618 ¯0.0021573
	<9○1⌷[2]!⌻∘⌻q ⍝ Quaternion number whose coefficients are ...		<9○1⌷[2]!⌻∘⌻q ⍝ Quaternion number whose coefficients are ...
	0.~~0060975i¯0~~.~~0010787j¯0~~.~~001618k¯0~~.0021573		0.0060975<_i/>¯0.0010787<_j/>¯0.001618<_k/>¯0.0021573
	!q		!q
	0.~~0060975i¯0~~.~~0010787j¯0~~.~~001618k¯0~~.0021573		0.0060975<_i/>¯0.0010787<_j/>¯0.001618<_k/>¯0.0021573
	</pre></apll>		</pre></apll>

WikiSysop at 20:46, 1 August 2019

2019-08-01T20:46:22Z

← Older revision		Revision as of 16:46, 1 August 2019
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	<table border="1" cellpadding="5" cellspacing="0" rules="none" summary="">		<table border="1" cellpadding="5" cellspacing="0" rules="none" summary="">
	<tr>		<tr>
	<td><apll>Z←<i>f</i>⌻R</apll></td>		<td valign="top"><apll>Z←<i>f</i>⌻R</apll></td>
	<td></td>		<td></td>
	<td></td>		<td></td>
Line 8:		Line 8:

	<tr>		<tr>
	<td><apll>Z←L <i>f</i>⌻R</apll></td>		<td valign="top"><apll>Z←L <i>f</i>⌻R</apll></td>
	<td></td>		<td></td>
	<td></td>		<td></td>
Line 15:		Line 15:

	<tr>		<tr>
	<td><apll>Z←∘⌻R</apll></td>		<td valign="top"><apll>Z←∘⌻R</apll></td>
	<td></td>		<td></td>
	<td></td>		<td></td>

WikiSysop at 00:37, 24 August 2017

2017-08-24T00:37:53Z

← Older revision		Revision as of 20:37, 23 August 2017
Line 85:		Line 85:

	⍝ Factorial of a Complex number		⍝ Factorial of a Complex number
	~~c←1J2~~		c←<⍳2
	∘⌻c ⍝ Matrix representation of a Complex number		∘⌻c ⍝ Matrix representation of a Complex number
	1 ¯2		1 ¯2
Line 102:		Line 102:

	⍝ Factorial of a Quaternion		⍝ Factorial of a Quaternion
	!<⍳4		q←<⍳4
			∘⌻q ⍝ Matrix representation of a Quaternion number
			1 ¯2 ¯3 ¯4
			2 1 ¯4 3
			3 4 1 ¯2
			4 ¯3 2 1
			!⌻∘⌻q ⍝ Matrix Factorial of ...
			0.0060975 0.0010787 0.001618 0.0021573
			¯0.0010787 0.0060975 0.0021573 ¯0.001618
			¯0.001618 ¯0.0021573 0.0060975 0.0010787
			¯0.0021573 0.001618 ¯0.0010787 0.0060975
			1⌷[2]!⌻∘⌻q ⍝ First column of ...
			0.0060975 ¯0.0010787 ¯0.001618 ¯0.0021573
			9○1⌷[2]!⌻∘⌻q ⍝ Real parts of ...
			0.0060975 ¯0.0010787 ¯0.001618 ¯0.0021573
			<9○1⌷[2]!⌻∘⌻q ⍝ Quaternion number whose coefficients are ...
			0.0060975i¯0.0010787j¯0.001618k¯0.0021573
			!q
	0.0060975i¯0.0010787j¯0.001618k¯0.0021573		0.0060975i¯0.0010787j¯0.001618k¯0.0021573
	</pre></apll>		</pre></apll>

WikiSysop at 14:37, 11 August 2017

2017-08-11T14:37:49Z

@@ Line 1: / Line 1: @@
 <table border="1" cellpadding="5" cellspacing="0" rules="none" summary="">
 <tr>
-   <td><apll>Z←f⌻R</apll></td>
+   <td><apll>Z←<i>f</i>⌻R</apll></td>
    <td></td>
    <td></td>
-   <td>applies the monadic function <apll>f</apll> to the (square) diagonalizable matrix <apll>R</apll> as a whole and returns the resulting matrix.  The shape of the result is <apll>⍴R</apll>.</td>
+   <td>applies the monadic function <apll><i>f</i></apll> to the (square) diagonalizable matrix <apll>R</apll> as a whole and returns the resulting matrix.  The shape of the result is <apll>⍴R</apll>.</td>
 </tr>
 <tr>
-   <td><apll>Z←Lf⌻R</apll></td>
+   <td><apll>Z←L <i>f</i>⌻R</apll></td>
    <td></td>
    <td></td>
-   <td>applies the monadic derived function <apll>L∘f</apll> to the (square) diagonalizable matrix <apll>R</apll> as a whole and returns the resulting matrix.  <apll>L</apll> is a scalar.  The shape of the result is <apll>⍴R</apll>.</td>
+   <td>applies the monadic derived function <apll>L∘<i>f</i></apll> to the (square) diagonalizable matrix <apll>R</apll> as a whole and returns the resulting matrix.  <apll>L</apll> is a scalar.  The shape of the result is <apll>⍴R</apll>.</td>
 </tr>
@@ Line 18: / Line 18: @@
    <td></td>
    <td></td>
-   <td>for scalar R, returns a (square) matrix representation of the Hypercomplex number <apll>R</apll>.  The shape of the result is <apll>2⍴=R</apll>.</td>
+   <td>for Hypercomplex scalar R, returns a (square) matrix representation of <apll>R</apll>.  The shape of the result is <apll>2⍴=R</apll>.</td>
 </tr>
@@ Line 25: / Line 25: @@
    <td></td>
    <td></td>
-   <td>for vector R, returns a (square) diagonal matrix with the items in <apll>R</apll> inserted into the diagonal.  <apll>R</apll> may be a simple or nested vector.  In the latter case, the items of <apll>R</apll> must be simple numeric scalars, vectors, or matrices.  The shape of the result is <apll>2⍴+/≢¨R</apll>.</td>
+   <td>for a simple or nested vector R, returns a (square) diagonal matrix with the items in <apll>R</apll> inserted into the diagonal.  For a nested vector <apll>R</apll>, its items must be simple numeric scalars, vectors, or matrices.  The shape of the result is <apll>2⍴+/≢¨R</apll>.</td>
 </tr>
 </table>

WikiSysop: Created page with "

Z←f⌻R applies the monadic function
2017-08-11T13:43:53Z

Created page with "<table border="1" cellpadding="5" cellspacing="0" rules="none" summary=""> <tr> <td><apll>Z←f⌻R</apll></td> <td></td> <td></td> <td>applies the monadic function <a..."

New page
<table border="1" cellpadding="5" cellspacing="0" rules="none" summary="">
<tr>
<td><apll>Z←f⌻R</apll></td>
<td></td>
<td></td>
<td>applies the monadic function <apll>f</apll> to the (square) diagonalizable matrix <apll>R</apll> as a whole and returns the resulting matrix. The shape of the result is <apll>⍴R</apll>.</td>
</tr>

<tr>
<td><apll>Z←Lf⌻R</apll></td>
<td></td>
<td></td>
<td>applies the monadic derived function <apll>L∘f</apll> to the (square) diagonalizable matrix <apll>R</apll> as a whole and returns the resulting matrix. <apll>L</apll> is a scalar. The shape of the result is <apll>⍴R</apll>.</td>
</tr>

<tr>
<td><apll>Z←∘⌻R</apll></td>
<td></td>
<td></td>
<td>for scalar R, returns a (square) matrix representation of the Hypercomplex number <apll>R</apll>. The shape of the result is <apll>2⍴=R</apll>.</td>
</tr>

<tr>
<td valign="top"><apll>Z←∘⌻R</apll></td>
<td></td>
<td></td>
<td>for vector R, returns a (square) diagonal matrix with the items in <apll>R</apll> inserted into the diagonal. <apll>R</apll> may be a simple or nested vector. In the latter case, the items of <apll>R</apll> must be simple numeric scalars, vectors, or matrices. The shape of the result is <apll>2⍴+/≢¨R</apll>.</td>
</tr>
</table>