Linear algebra is the foundation of machine learning. Most machine learning data is represented as vectors, matrices, or tensors, so linear algebra is heavily relied upon. Vectors are 1D arrays that represent points with magnitude and direction. Matrices are 2D arrays of numbers with fixed rows and columns. Tensors generalize vectors and matrices by allowing more than two dimensions, such as 3D images with RGB values. Key concepts in linear algebra include eigenvectors, which are vectors only scaled by a matrix, and eigenvalues, which are the scaling factors.

1. Linear Algebra for Machine
Learning basics

2. Why do you need to learn Linear algebra?
• Linear algebra is a foundation of machine learning. Before you
start to study machine learning, you need to get better knowledge
and understanding of this field

3. Vectors, Matrices, and Tensors
• In machine learning, the majority of data is most often
represented as vectors, matrices or tensors. Therefore, the
machine learning heavily relies on the linear algebra.

4. A vector
• A vector is a 1D array. For instance, a point in space can be
defined as a vector of three coordinates (x, y, z). Usually, it is
defined in such a way that it has both the magnitude and the
direction.

5. A matrix
• A matrix is a two-dimensional array of numbers, that has a fixed
number of rows and columns. It contains a number at the
intersection of each row and each column. A matrix is usually
denoted by square brackets [].

7. Tensors
• A tensor is a generalization of vectors and matrices. For instance,
a tensor of dimension one is a vector. In addition, we can also
have a tensor of two dimensions which is a matrix. Then, we can
have a three-dimensional tensor such as the image with RGB
colors. This continues to expand to four-dimensional tensors and
so on.

9. Linear Algebra examples

13. Eigenvector and eigenvalue
• Any vector that is only scaled by a matrix is called
an eigenvector of that matrix. And how much the vector is
scaled we call the eigenvalue.

14. Eigenvector and eigenvalue