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Abstract definition of matrix multiplication

In the following tables, matrix A represents the quantities of the materials P and Q to produce products M and N. Matrix B represents the prices of the materials P and Q of the suppliers C1 and C2.

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       }}} C1 {{{       

       }}} C2 {{{       

       }}} P {{{       

       }}} p {{{       

       }}} q {{{       

       }}} Q {{{       

       }}} r {{{       

       }}} s {{{       

Blocking

The matrix multiplication of the original arrays can be transformed into matrix multiplication of blocks. For example,

C_block(1,1)=A_block(1,1)*B_block(1,1) + A_block(1,2)*B_block(2,1)

+-----+-----+     +-----+-----+   +-----+-----+
| x x |     |     | --> | --> |   | | | |     |
| x x |     |     | --> | --> |   | ↓ ↓ |     |
+-----+-----+  =  +-----+-----+ * +-----+-----+
|     |     |     |     |     |   | | | |     |
|     |     |     |     |     |   | ↓ ↓ |     |
+-----+-----+     +-----+-----+   +-----+-----+