Welcome to a new set of blog posts that will explore Linear algebra.

At its core, linear algebra is a branch of mathematics that deals with:

Vectors: These are quantities that have both a magnitude and a direction, like arrows.

Vector Spaces: These are sets of vectors that follow certain rules. You can add vectors together and multiply them by numbers in a specific way within a vector space.

Linear Independence: A set of vectors is linearly independent. You can’t make one vector by combining others in the set.

Basis: A basis is a set of special vectors. These vectors can be used to represent any vector in a vector space.

Linear Transformations: These are functions that change vectors while keeping certain rules intact, like preserving straight lines.

Matrices: These are rectangular grids of numbers used to represent linear transformations and solve systems of equations.

Eigenvalues and Eigenvectors: These are important properties of matrices with applications in various fields.

Inner Product and Dot Product: These are ways to measure angles between vectors.

Determinants: These are values associated with matrices that tell us important things about them.

Linear algebra is widely used in physics, engineering, computer science, and economics. It solves problems related to vectors, transformations, and equations. It’s a fundamental tool in many areas of science and technology.

Enjoy!