Study Guide

Objective

You learn fundamental mathematical concepts, principles, tools (including computing environments) and terminology for professional studies in the field of machine learning and data engineering. You are familiar with the basic principles and methods of vector and matrix calculus and can apply them. You can use vectors and matrices to solve problems related to your professional field. You are able to utilize numerical computation methods.

You master the basic vector operations. You can use vectors to solve geometrical problems. You understand the principles of modeling physical phenomena using vectors. You can distinguish between linearly dependent and independent vectors.

You can perform basic operations with matrices and calculate matrix products, determinants, and inverse matrices. You can solve linear systems of equations using matrix calculus methods. You become familiar with applications of matrix calculus and perform linear regression using matrice notation.

Content

Basic concepts, operations and special types of vectors and matrices
Vector spaces, linear combinations of vectors, span
Vector representation by basis vectors and polar coordinates
Dot product, projections, cross product, and scalar triple product and their applications
Linear dependency
Systems of linear equations
Determinants and inverse matrix
Linear mappings
Linear regression

Assessment criteria, satisfactory (1)

You can perform basic operations with vectors and matrices, such as addition and scalar multiplication. You can solve basic and well-defined problems using vectors and matrices and you are able solve a pair of linear equations.

Assessment criteria, good (3)

You can perform various calculations with vectors and matrices. You can use the methods of vector and matrix calculus to solve versatile problems, such as finding determinants, inverses, and solving systems of linear equations.

Assessment criteria, excellent (5)

You can perform complex calculations with vectors and matrices. You are able to prove if vectors are linearly independent or not. You can conduct a linear regression. You are able to apply the methods of linear algebra in solving and handling new types of problems.