Tensor operation refers to the process of performing various mathematical operations on tensor. Tensor is a higher dimensional array, which can be regarded as the generalization of vector and matrix. Unlike vectors and matrices, tensors can have arbitrary dimensions. Tensor operations include scalar multiplication, vector addition, matrix multiplication and other basic operations, as well as more advanced tensor products, outer products, inner products and other operations. Tensor operations are widely used in physics, engineering, computer science and other fields, such as describing the motion state of objects, image processing, machine learning and so on.
Matrix operation refers to the process of performing various mathematical operations on matrices. Matrix is a two-dimensional array composed of rows and columns, which can be regarded as a generalization of vectors. Matrix operations include basic operations such as matrix addition, matrix subtraction and matrix multiplication, as well as more advanced operations such as inverse matrix, determinant and eigenvalue. Matrix operations are widely used in linear algebra, calculus, optimization theory and other fields, such as solving linear equations, calculating derivatives and solving optimization problems.
There are some connections and differences between tensor operation and matrix operation. First of all, tensor and matrix are basic objects in linear algebra, and they can perform similar mathematical operations. Secondly, the dimension of tensor is higher than that of matrix, which can represent more complex data structures. However, with the increase of tensor dimension, the computational complexity of tensor operation will increase accordingly. In addition, tensor operation and matrix operation are also different in some specific operations, such as the definition and properties of tensor product and matrix multiplication.
In a word, tensor operation and matrix operation are two important linear algebraic operations in mathematics, which are widely used in various fields. By mastering these operations, we can better understand and solve practical problems.