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--- public:calculator:guides:dm41x_matrix [07/02/26 20:31 GMT] – [Example Definition] john
+++ public:calculator:guides:dm41x_matrix [08/02/26 08:26 GMT] (current) – [Example Definition] john
@@ Line 36: / Line 36: @@
 |C|''CMEDIT''|K| |
 |D|''MINV''|L| |
-|E|''M*M''|M| |
+|E|''M*M''|M|''ZK?YN''|
 |F|''MDET''|N|''EMDIR'' |
 |G|''TRNPS''|O|''EMDIRX''|
 |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 =====
@@ Line 183: / Line 183: @@
   * Put the matrix names in ''ALPHA'' in the form ''Matrix 1,Matrix2,Results Matrix''
     * ''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
     * <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.
@@ Line 359: / Line 359: @@
 ''
-Two rows and two columns containing complex numbers, so the definition/dimension is ''4.004''
+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
@@ Line 370: / Line 370: @@
 ''
-The entry is via ''CMEDIT'' which asks for each ''Real'' and ''Imaginary'' part in turn
+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='' ''1'' <key>'R/S'</key>
+    * ''RE. 1:1='' <key>1</key> <key>'R/S'</key>
-    * ''IM. 1:1='' ''2'' <key>'R/S'</key>
+    * ''IM. 1:1='' <key>2</key> <key>'R/S'</key>
-    * ''RE. 1:2='' ''5'' <key>'R/S'</key>
+    * ''RE. 1:2='' <key>5</key> <key>'R/S'</key>
-    * ''IM. 1:2='' ''6'' <key>'R/S'</key>
+    * ''IM. 1:2='' <key>6</key> <key>'R/S'</key>
-    * ''RE. 2:1='' ''3'' <key>'R/S'</key>
+    * ''RE. 2:1='' <key>3</key> <key>'R/S'</key>
-    * ''IM. 2:1='' ''4'' <key>'R/S'</key>
+    * ''IM. 2:1='' <key>4</key> <key>'R/S'</key>
-    * ''RE. 2:2='' ''7'' <key>'R/S'</key>
+    * ''RE. 2:2='' <key>7</key> <key>'R/S'</key>
-    * ''IM. 2:2='' ''8'' <key>'R/S'</key>
+    * ''IM. 2:2='' <key>8</key> <key>'R/S'</key>
 ==== Multiplication of Complex Matrices ====
-Create a second matrix ''B'' of ''2x1'' which can be multiplied by ''A'' as ''A'' x ''B''
+=== Create a second matrix ===
+  * Matrix ''B'' of size ''2x1'' which can be multiplied by ''A'' as ''A'' x ''B''
 ''
@@ Line 393: / Line 395: @@
 ''
-Dimension ''4.002''
+=== 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='' ''3'' <key>'R/S'</key>
+    * ''RE. 1:1='' <key>3</key> <key>'R/S'</key>
-    * ''IM. 1:1='' ''4'' <key>'R/S'</key>
+    * ''IM. 1:1='' <key>4</key> <key>'R/S'</key>
-    * ''RE. 2:1='' ''2'' <key>'R/S'</key>
+    * ''RE. 2:1='' <key>2</key> <key>'R/S'</key>
-    * ''IM. 2:1='' ''6'' <key>'R/S'</key>
+    * ''IM. 2:1='' <key>6</key> <key>'R/S'</key>
-Create a result matrix 'C' which will be a 2x1 complex with dimension ''4.002''
+=== 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
+=== Multiply A X B = C ===
-  * <key>ALPHA</key> <key>'A,B,C'</key>
+  * <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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