---- > [!definition] Definition. ([[truncated svd]]) > For a [[matrix]] $A \in \mathbb{F}^{M \times N}$, the **truncated SVD** of $A$ is given by removing terms from the [[outer product formulation of the SVD|outer product SVD]] of $A$ corresponding to 'small' [[singular values]]: $\sum_{k=1}^{K}\sigma_{k}v_{k}u_{k}',$ > where the $\{ \sigma_{i} \}_{i=1}^{K}$ denote the first $K$ [[singular values]] of $A$. > \ > $K$ is a [[hyperparameter]] whose value is less than the [[rank]] of $A$. ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```