The Simple Gift, Numb, and The Matrix

Humans naturally want to establish a connection with others and gain self-worth. Many factors are involved in these relationships. The free novel "Steven Herrick's Simple Gift", the song of Lincoln Park Numb, and the movie "The Matrix" all show that some people intentionally cut off connections with others. Their own personality, the choice of people's lives will prevent or assist them from establishing contact with others, and the measure of one of their degrees will be their popularity or social It depends on status.

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 and should not actually be used 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.