In mathematics, the complexification of a vector space over the field of real numbers (a "real vector space") yields a vector space over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers. Any basis for (a space over the real numbers) may also serve as a basis for over the complex numbers.
數學中,實數域上的向量空間V的複化是在複數域上對應的向量空間VC,就是說它有與V相同的維數,V在實數域上的基可以作為VC在複數域上的基。 例如設V包含m×n實矩陣,則VC包含m×n複矩陣。 不依賴於基的定義是取V和複數在實域上的張量積: 。 複向量空間有額外結構:典範複共軛運算。因為以包含在內,複共軛運算可定義為。這運算常記作或。 相反地,給出複向量空間,並有複共軛運算,作為複向量空間同構於的實子空間的複化。也就是說,所有帶有複共軛運算的複向量空間都是實向量空間的複化。 例如有標準共軛運算,那麼。
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Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).