Today's data management systems increasingly need to support both tensor-algebraic operations (for analysis) as well as relational-algebraic operations (for data manipulation and integration). Tensor decomposition techniques are commonly used for discovering underlying structures of multidimensional data sets. However, as the relevant data sets get large, existing in-memory schemes for tensor decomposition become increasingly ineffective and, instead, memory-independent solutions, such as in-database analytics, are necessitated. We introduce an in-database analytic system for efficient implementations of in-database tensor decompositions on chunk-based array data stores, so called, TensorDB. TensorDB includes static in-database tensor decomposition and dynamic in-database tensor decomposition operators. TensorDB extends an array database and leverages array operations for data manipulation and integration. TensorDB supports complex data processing plans where multiple relational algebraic and tensor algebraic operations are composed with each other.