If matrix A can be similar to diagonal matrix, then diagonal elements of diagonal matrix are N eigenvalues of A, and column vectors of invertible matrix P are N linearly independent eigenvectors corresponding to these eigenvalues. The first non-zero element of each non-zero row is 1, and the other elements in the column where the first non-zero element of each non-zero row is located are all zeros, which is the simplest matrix.
If the upper left corner of a matrix is identity matrix, then the elements in other positions are all zeros. You can draw a trapezoidal line in the matrix, with all zeros under it and only one line in each step. The number of steps is the number of non-zero lines, and the first element behind the vertical lines of the ladder line (each vertical line is one line in length) is a non-zero element, that is, the first non-zero element of the non-zero line, so this matrix is called a row ladder matrix.
Matrix history
The concept of matrix was gradually formed in19th century. 1800, gauss and William Jordan established gauss-Jordan elimination method. 1844 The German mathematician Ferdinand Eisenstein discussed the transformation (matrix) and its product. 1850, the English mathematician james joseph sylvester first used the word matrix.
British mathematician Arthur Kelly is recognized as the founder of matrix theory. When he began to study the matrix as an independent mathematical object, he had found many properties related to moments in the study of determinant, which made Kelly think that the introduction of matrix was very natural. 1854, the French mathematician Hermite used the term orthogonal matrix, but his formal definition was not published by Philo Behnes until 1878. In 1879, Ferrobenius introduced the concept of matrix rank.
Refer to the above content: Baidu Encyclopedia-Matrix