The multiplication operator can be used as follows:
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The meaning of this operation depends on the tensorial orders of and . The various possibilities are summarized in Table I.4.8 with a short explanation of the meaning of the operation when deemed necessary.
| meaning | |||
| S | S | S | — |
| V | S | V | — |
| M | S | M | — |
| V | V | S | — |
| S | V | V | scalar product of two vectors |
| V | V | M | left multiplication of a matrix by a vector |
| M | M | S | — |
| V | M | V | right multiplication of a matrix by a vector |