Linear algebra begins with vectors, then progresses to matrices and then subspaces. Vectors are used in linear combinations-- this is the key thing you can do with them. A matrix is a set of vectors ...

Just like a solid foundation is essential to a building, linear algebra forms an essential learning segment for machine learning (ML). Areas of mathematics such as statistics and calculus require ...

This course focuses on lines and planes, the geometry and algebra of vectors, systems of linear equations, matrix algebra, linear independence, spanning sets, basis, linear transformations, ...

Now we are ready to see how matrix algebra can be useful when analyzing data. We start with some simple examples and eventually arrive at the main one: how to write linear models with matrix algebra ...

Abstract: The book consists of three parts. Part 1 focuses on vectors and their manipulation. Vector algebra, linear functions, linearization, inner products, norms, linear independence, the concept ...

I said that in a field, you have to be able to divide by non-zero elements. Let’s check this is true in these two examples. Being able to divide by \(x\) is equivalent to the existence of an element \ ...

Simultaneous equations are two or more equations with two or more variables. They are simultaneous because they can be solved to give values for the variables that are equal in each equation. In the ...

An equation is a mathematical statement showing that two expressions are equal. Equations can be solved by finding values (solutions) which make the statement true. A linear equation has no terms ...