# Subspace **Space** is short for **subspace**. A **subspace** is a subset that is **“closed”** under addition and scalar multiplication, which is basically closed under **linear combinations**. These two operations keep the output **within** the subspace always. ### Definition (formal) A subspace of a vector space is a subset that satisfies the requirements for a vector space -- Linear combinations stay in the subspace.(i) If any two vectors **x** and **y** are in the subspace, **x + y** is in the subspace as well.(ii) If we multiply any vector **x** in the subspace by any scalar **c**, **cx** is in the subspace as well. --- Date: 20220115 Links to: Tags: References: * []()