**Overview**

Linear algebra is the most important and basic part of mathematics. Its only serious competitor is the calculus. There are a wide range of applications, such as inside other parts of math itself, outside of problems that occur outside math. One of the reasons for this importance is that so many non-linear transformations can be effectively approximated by linear transformations and are well understood by studying these approximations. The other is the complexity of understanding linear transformations and the matrices that implement them. It is well known that matrices can be reduced to a special (standard) form whose behavior is easy to understand. In addition, linear algebra course online for credit provides inspiration and useful examples for many advanced abstract algebras.

It’s naive to start the course by showing how to solve any system of linear equations and describe the set of all its solutions. Once this is well understood, it can serve as a potential topic for the rest of the course, such as in simplifications that make the computation of determinants numerically feasible, in computing orthonormal bases, in articulating with eigenvalues and eigenvectors in spectral theory. This is the first course that utilizes linear changes in coordinates for simplification.

**Recommended reading**

The Continuing Education Library has provided scanned materials to support your course*, which are provided along with other reading list materials in your virtual classroom atthe request of your instructor. Students can also explore a variety of free online resources through the Library Catalog SOLO. See the guide for more information if you live close enough to visit the continuing education library directly, we recommend that you become a member of the library and borrow books or use a computer.

**Certification**

Students enrolled for CATS points will receive a CATS point record upon successful completion of the course assessment. To earn credits (CATS points) you need to register and pay an additional £10 fee per course. You can do this by ticking the relevant box at the bottom of the registration form or when you register online. Coursework is an integral part of all weekly classes and everyone who enrolls should complete the coursework in order to fully benefit from the course. Only those registered for credit will receive CATS credits for work performed to the required standards.

Students who are not registered for CATS credits during the registration process can register for CATS credits prior to the start of the course or retrospectively on January 1st after the completion of the current full academic year. If you are registered for a higher education certificate, you will need to indicate this on the registration form, but there is no additional registration fee.

**Course objectives**

Familiar with the language and notation of linear algebra.

Have a comprehensive understanding of systems of linear equations and their solutions.

Master basic matrix algebra.

Vector space basics: linear combination, generation, basis.

Be able to find a matrix representing a given linear transformation with respect to a given basis.

**Teaching method**

Distance Calculus provides students with Homework problems and lectures that mix solutions with theory, examples, and exercises.

**Learning result**

At the end of the course, students should:

Know how to solve the linear equations m in the n sign and what the set of all solutions “looks”.

Proficient in matrix arithmetic.

Be able to calculate non-unique examples and correctly apply the standard theorems of basic linear algebra.

**Evaluation method**

There are several tests designed to understand that basic facts are in students’ heads, not just in their notes. Students must submit a completed author declaration form covering the submitted test. Without the above form, CATS points cannot be earned.

**Basic Reasons for learning linear algebra for machine learning**

**1. You need to learn linear algebra notation**

You must be able to read and write vector and matrix symbols. Algorithms are described in books, papers, and websites using vector and matrix notation. Linear algebra is the mathematics of data, and symbols allow you to precisely describe operations on data using specific operators. You need to be able to read and write this symbol. This skill will allow you to:

· Read descriptions of existing algorithms in textbooks.

Interpret and implement the description of the new method in the research paper.

Briefly describe your own approach to other practitioners.

Additionally, programming languages such as Python provide an efficient way to directly implement linear algebra notation.

An understanding of notation and how it is implemented in your language or library will allow for shorter and potentially more efficient implementations of machine learning algorithms.

**2. You need to learn linear algebra arithmetic**

Arithmetic operations are performed with symbols from linear algebra. A challenge for newcomers to the field of linear algebra is that operations such as matrix multiplication and tensor multiplication are not implemented as direct multiplications of these structuring elements, which may seem unintuitive at first glance. Again, most, if not all, of these operations are efficiently implemented and provided via API calls in modern linear algebra libraries.As part of being able to effectively read and write matrix symbols, you need to understand how vector and matrix operations are implemented.

**3. You need to learn statistical linear algebra**

You have to learn linear algebra to learn statistics especially multivariable statistics. Statistics and data analysis are other areas of mathematics that underpins machine learning. As the mathematics of data, linear algebra has made its mark in many related fields of mathematics, including statistics. To be able to read and interpret statistics, you must learn the symbols and operations of linear algebra.

Modern statistics uses both textual and algebraic tools to describe the tools and techniques of statistical methods from the mean and diversity of data meanings, to coexistence diagrams that define the relationship between Gaussian variables. The results of the collaboration between the two sites are also an important part of machine learning, as the analysis of the most important part of data reduction or short PCA.