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public:calculator:guides:dm41x_matrix [07/02/26 20:05 GMT] – [Another way to solve a system] johnpublic:calculator:guides:dm41x_matrix [08/02/26 08:26 GMT] (current) – [Example Definition] john
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 |C|''CMEDIT''|K| | |C|''CMEDIT''|K| |
 |D|''MINV''|L| | |D|''MINV''|L| |
-|E|''M*M''|M| |+|E|''M*M''|M|''ZK?YN''|
 |F|''MDET''|N|''EMDIR'' | |F|''MDET''|N|''EMDIR'' |
 |G|''TRNPS''|O|''EMDIRX''| |G|''TRNPS''|O|''EMDIRX''|
 |H|''MSYS''|P|''PURFL''| |H|''MSYS''|P|''PURFL''|
  
-Matrices are saved in Extended Memory, and I put commands in CST to find and remove them once I'm finished: ''EMDIR'', ''EMDIRX'' and ''PURFL''+Matrices are saved in Extended Memory, and I put commands in CST to find and remove them once I'm finished: ''EMDIR'', ''EMDIRX'' and ''PURFL'' and I have ''ZK?YN'' to quickly access [[41z_module|]] complex number functions (assuming the module is //plugged-in//).
  
 ===== Basic Workflow ===== ===== Basic Workflow =====
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   * Put the matrix names in ''ALPHA'' in the form ''Matrix 1,Matrix2,Results Matrix''   * Put the matrix names in ''ALPHA'' in the form ''Matrix 1,Matrix2,Results Matrix''
     * ''ALPHA'' = ''A,B,C''     * ''ALPHA'' = ''A,B,C''
-  * <key>ALPHA</key> <key>'A'</key> <key>','</key> <key>'B'</key> <key>','</key><key>'C'</key><key>ALPHA</key>+  * <key>ALPHA</key> <key>'A'</key> <key>','</key> <key>'B'</key> <key>','</key> <key>'C'</key><key>ALPHA</key>
   * Execute ''M*M'' from the ''CST'' menu   * Execute ''M*M'' from the ''CST'' menu
     * <key>CST</key> <key>'E'</key>     * <key>CST</key> <key>'E'</key>
Line 344: Line 344:
  
  
-===== Complex Matrix =====+===== The Complex Matrix ===== 
 + 
 +It is possible to define, edit and carry out operations with matrices containing Complex Numbers. 
 + 
 +The matrix is defined with **twice as many rows and columns** as appears necessary, and edited with the function ''CMEDIT'', in ''CST'' menu ''C'' 
 + 
 + 
 +==== Example Definition ==== 
 + 
 + 
 +'' 
 +| 1+j2  5+j6 | 
 +| 3+j4  7+j8 | 
 +'' 
 + 
 +Two rows and two columns ''2x2'' containing complex numbers, so the definition/dimension is ''4.004'' 
 + 
 +The numbers are actually saved as if in a larger real matrix as 
 + 
 +'' 
 +| 1 -2  5 -6 | 
 +| 2  1  6  5 | 
 +| 3 -4  7 -8 | 
 +| 4  3  8  7 | 
 +'' 
 + 
 +The entry is via ''CMEDIT'' via ''CST'' menu ''C'', which asks for each ''Real'' and ''Imaginary'' part in turn 
 + 
 +  * <key>ALPHA</key> <key>'A'</key> <key>ALPHA</key> 
 +  * ''4.004'' <key>'CST'</key> <key>'A'</key> 
 +  * <key>'CST'</key> <key>'C'</key> 
 +    * ''RE. 1:1='' <key>1</key> <key>'R/S'</key> 
 +    * ''IM. 1:1='' <key>2</key> <key>'R/S'</key> 
 +    * ''RE. 1:2='' <key>5</key> <key>'R/S'</key> 
 +    * ''IM. 1:2='' <key>6</key> <key>'R/S'</key> 
 +    * ''RE. 2:1='' <key>3</key> <key>'R/S'</key> 
 +    * ''IM. 2:1='' <key>4</key> <key>'R/S'</key> 
 +    * ''RE. 2:2='' <key>7</key> <key>'R/S'</key> 
 +    * ''IM. 2:2='' <key>8</key> <key>'R/S'</key> 
 + 
 +==== Multiplication of Complex Matrices ==== 
 + 
 +=== Create a second matrix === 
 + 
 +  * Matrix ''B'' of size ''2x1'' which can be multiplied by ''A'' as ''A'' x ''B'' 
 + 
 +'' 
 +| 3+j4 | 
 +| 2+j6 | 
 +'' 
 + 
 +=== Dimension second matrix === 
 + 
 +This is dimensioned as double the basic size of ''2x1'' : ''4.002'' and then populated with ''CMEDIT'' 
 + 
 +  * <key>ALPHA</key> <key>'B'</key> <key>ALPHA</key> 
 +  * ''4.002'' <key>'CST'</key> <key>'A'</key> 
 +  * <key>'CST'</key> <key>'C'</key> 
 +    * ''RE. 1:1='' <key>3</key> <key>'R/S'</key> 
 +    * ''IM. 1:1='' <key>4</key> <key>'R/S'</key> 
 +    * ''RE. 2:1='' <key>2</key> <key>'R/S'</key> 
 +    * ''IM. 2:1='' <key>6</key> <key>'R/S'</key> 
 + 
 +=== Create a result matrix === 
 + 
 +Matrix 'C' which will be also be a ''2x1'' complex with dimension :''4.002'' 
 + 
 +  * <key>ALPHA</key> <key>'C'</key> <key>ALPHA</key> 
 +  * ''4.002'' <key>'CST'</key> <key>'A'</key> 
 + 
 +=== Multiply A X B = C === 
 + 
 +  * <key>ALPHA</key> <key>'A'</key> <key>','</key> <key>'B'</key> <key>','</key> <key>'C'</key> <key>ALPHA</key> 
 +  * <key>'CST'</key> <key>'E'</key> 
 + 
 + 
 +=== Inspect Result Matrix C === 
 + 
 +  * <key>ALPHA</key> <key>'C'</key> 
 +  * <key>'CST'</key> <key>'C'</key> 
 +    * ''RE. 1:1= -31.000'' <key>'R/S'</key> 
 +    * ''IM. 1:1=  52.000'' <key>'R/S'</key> 
 +    * ''RE. 2:1= -41.000'' <key>'R/S'</key> 
 +    * ''IM. 2:1=  82.000'' <key>'R/S'</key> 
 + 
 +The result matrix is therefore 
 + 
 +'' 
 +| -31+j52 | 
 +| -41+j82 | 
 +'' 
 + 
 +Which agrees with my long-hand calculation (thanks to [[41z_module|]] ) 
 + 
 + 
 +'' 
 +|(1+j2).(3+j4) + (5+j6).(2+j6)| 
 +|(3+J4).(3+J4) + (7+J8).(2+J6)| 
 +'' 
 + 
 +'' 
 +| (-5+j10) + (-26+j42) | 
 +| (-7+j24) + (-34+j58) | 
 +'' 
 + 
 +'' 
 +| -31+j52 | 
 +| -41+j82 | 
 +'' 
 +==== Systems of Complex Equations.... ==== 
 + 
 +Once you can enter and manipulate Complex Matrices you can also use ''MSYS'' to solve systems with complex matrices in the same way as usual - the only difference is entering the matrices as Complex. 
 + 
  
  

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