1. **Vector Space:** A set of vectors where you can add any two vectors and multiply vectors by scalars, and the results stay in the set. 2. **Subspace:** A smaller vector space inside a bigger one that follows the same rules (closed under addition and scalar multiplication). 3. **Linearly Independent/Dependent Vectors:** Vectors are independent if no vector can be made by combining others; dependent if at least one can be made from others. 4. **Basis and Dimension:** A basis is a set of independent vectors that can create every vector in the space. Dimension is how many vectors are in the basis. 5. **Linear Transformation:** A function that takes vectors from one space to another, keeping addition and scalar multiplication rules. 6. **Dot Product – Orthogonality:** Dot product measures how much two vectors point in the same direction. If dot product is zero, vectors are orthogonal (at right angles). 7. **Eigenvalues – Eigenvectors:** For a transformation, eigenvectors are special vectors that only get stretched or shrunk (not rotated). The amount they stretch/shrink is the eigenvalue. This is a brief and simple overview of these key vector space concepts.