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pre-hilbert_space [2013/08/31 20:42] nikolaj |
pre-hilbert_space [2013/08/31 20:56] nikolaj |
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| | @#55EE55: $\langle a\cdot v+b\cdot w | u \rangle = \overline a\cdot \langle v|u \rangle+\overline b \cdot \langle w|u \rangle $ | | | @#55EE55: $\langle a\cdot v+b\cdot w | u \rangle = \overline a\cdot \langle v|u \rangle+\overline b \cdot \langle w|u \rangle $ | | ||
| - | ==== Ramifications ==== | + | ==== Discussion ==== |
| - | === Discussion === | + | |
| - | A vector space is a $F$-module over $V$, where $F$ is a field, not just a ring. | + | |
| - | + | ||
| - | One speaks of an $F$-vector space over $V$. Here $F$ and $V$ are just sets. | + | |
| ==== Reference ==== | ==== Reference ==== | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Inner_product_space|Inner product space]] | Wikipedia: [[http://en.wikipedia.org/wiki/Inner_product_space|Inner product space]] | ||
| ==== Context ==== | ==== Context ==== | ||
| - | === Subset of === | + | === Refinement of === |
| [[Vector space]] | [[Vector space]] | ||
| === Requirements === | === Requirements === | ||
| [[Complex number]] | [[Complex number]] | ||
