Definition:Scalar Product


 * Scalar Multiplication: the operation of multiplying a vector $\mathbf a$ by a scalar $\lambda$ to form a new vector $\lambda \mathbf a$.


 * Dot Product: the operation $\mathbf a \cdot \mathbf b$ whereby two vector quantities $\mathbf a$ and $\mathbf b$ of the same dimension are combined to form a scalar.


 * Inner Product: the operation $\innerprod {\mathbf a}{\mathbf b}$ whereby two vectors $\mathbf a, \mathbf b$ in the same vector space are combined to form a scalar.


 * Nondegenerate Symmetric Bilinear Form