Regarding expansion of bilinear form relative to basis

Question

Let $X$ and $Y$ be vector spaces with basis $\{x_1, x_2,\cdots, x_n\}$ and $\{y_1, y_2,\cdots, y_n\}$ respectively and $\mathbb{K}$ be the real and complex field. Let $B:X\times Y\longrightarrow \mathbb{K}$ be a bilinear map. Then is it true that there exists linear maps $\phi_j:X\longrightarrow \mathbb{K}$ and $\psi_j:X\longrightarrow \mathbb{K}$ for $1\leq j\leq n$, such that $$B(x,y)=\sum_{1}^{n}\phi_j(x)\psi_j(y)$$ for every $(x,y)\in X\times Y$?