The Matrix

The matrix "Western" has never been known as a title. The matrix is ​​not determined to be Western, but there are good reasons for having to process the matrix in the same context. The kind of this movie is immersed in tradition and legend. There are many definitions as to what might constitute a "Western movie". The main goal is to see if you can explain the future type in this whitepaper. Whether it is the 20th century, the 21st century is still a faraway future. This type can move in larger, more exciting directions.

The transpose of the matrix product takes a simple form. (AB) '= B'A'. The inverse of A is expressed as A ^ -1 and is defined as a matrix like A ^ -1 A = I (I is the identity matrix). However, A ^ -1 is mainly used as a theoretical tool, so please do not actually use it in most software applications. Because A ^ -1 can only be represented with limited precision in digital computers, the algorithm is often able to obtain a more accurate estimate of x using the value of b. Many mathematical objects can be better understood by dividing them into components, or finding their common characteristics, rather than a way to express them. For example, an integer can be broken down into prime factors. The number 12 depends on whether it is decimal or binary, but 12 = 2 × 2 × 3 always applies.

A well-known matrix decomposition method is singular value decomposition (SVD). At higher levels, SVD is an algorithm that decomposes matrix A into the best low rank (ie, smaller / simpler) approximation of the original matrix A. Mathematically, we break up A into two unitary matrices and diagonal matrices. Where A is the input data matrix (user evaluation), U is the left singular vector (user's "feature" matrix) and Sum is a singular value pair. Angle matrix (basically the weight / intensity of each concept) V ^ T is the right singular vector (the "feature" matrix of the movie). U and V ^ T are column orthogonal and represent different things. U indicates the degree to which the user "likes" each function, and V ^ T indicates to what extent each function is related to each movie.

Let A be an m × n matrix. We define U as an m × m matrix, D as an m × n matrix, and V as an n × n matrix. Each of these matrices is defined as having a special structure. Both matrices U and V are defined as orthogonal matrices. The matrix D is defined as a diagonal matrix. Please note that D is not necessarily a square. The diagonal element of D is called the singular value of matrix A. The U column is called the left singular vector. Right singular vector