Linear algebra is the mathematics of data. It is about Linear Combinations. **Vectors** and **matrices** are the language of data. Using arithmetic on columns of numbers called Vectors and arrays of numbers called matrices to create new columns and arrays of numbers. Linear algebra is the study of lines and planes, vector spaces and mappings that are required for linear transforms - Dependence on GPUs is because of their ability to compute linear algebra operations fast for ML applications - Efficient implementations of vector and matrix multiplications were originally implemented in the FORTRAN programming language 3 popular open source numerical linear algebra libraries that implement these functions are: - Linear Algebra Package, or LAPACK. - Basic Linear Algebra Subprograms, or BLAS (a standard for linear algebra libraries). - Automatically Tuned Linear Algebra Software, or ATLAS. ### Applications - **Matrices** in Engineering, such as a line of springs. - **Graphs and Networks**, such as analyzing networks. - Markov Matrices, Population, and Economics, such as population growth. - Linear Programming, the simplex optimization method. - Fourier Series: Linear Algebra for functions, used widely in signal processing. - Linear Algebra for statistics and probability, such as least squares for regression. - Computer Graphics, such as the various translation, rescaling and rotation of images. Another interesting application of linear algebra is that it is the type of mathematics used by Albert Einstein in parts of his **theory of relativity**. Specifically tensors and tensor calculus. He also introduced a new type of linear algebra notation to physics called Einstein notation, or the Einstein summation convention.