| # Vector Scalar Product Vectors > Basics | Scalar product | Norms | Projection on a line | Orthogonalization | Hyperplanes | Linear functions | Application Definitions Orthogonality ## Definitions The scalar product (or, inner product, or dot product) between two vectors is the scalar denoted , and defined as The motivation for our notation above will come later, when we define the matrix-vector product. The scalar product is also sometimes denoted , a notation which originates in physics. Matlab syntax
    >> x = [1; 2; 3]; y = [4; 5; 6];
    >> scal_prod = x'*y;
Examples: Rate of return of a financial portfolio. Sample and weighted average. Beer-Lambert law in absorption spectroscopy. ## Orthogonality We say that two vectors are orthogonal if . Example: Two orthogonal vectors in .