Matrix 1 v.s. Matrix 3

After reading "Matrix Revolution", I was disappointed. The first movie was very well done, there are many characters, many people lost their story, they lost a lot of good actors. When they return to the real world, as the machine fight begins, it continues, Neo and Trinity disappear for a long time. Battle scenes never disappear for so long, eventually becoming ugly.

Tensors are usually considered generalized matrices. That is, a 1-D matrix (a vector is actually such a tensor), a 3-D matrix (a cube similar to a number), even a 0-D matrix (a single number) You can. It is more difficult to visualize. The dimension of a tensor is called its rank. Suppose there is a 3 node layer hidden in the neural network. Data flows into them via their ReLU function and then pops up some values. For clarity, we will set 2.5, 4, and 1.2 respectively. The output of these nodes can be represented as a vector.

The adjacency matrix is ​​a matrix representation that accurately represents on which nodes in the graph the edges between them are contained. The matrix looks a bit like a lookup table. If we decide we want to find the two nodes of the edge between them, the value is displayed at the intersection of the two nodes. The value of the adjacency matrix is ​​similar to the Boolean flag indicator, either existing or nonexistent. A value of 1 indicates that there is an edge between the two nodes, and if the value is 0, there is no edge between them.

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.