Rank of matrix意思

"Rank of a matrix" is a term from linear algebra that refers to the dimension of the largest linearly independent set of vectors that can be obtained from the columns or rows of a matrix. In other words, it is the number of linearly independent rows or columns of a matrix.

The rank of a matrix is an important concept because it determines the number of linearly independent equations in a system of linear equations, and it also plays a crucial role in the study of linear transformations and their properties.

The rank of a matrix can be found using various methods, including Gaussian elimination, the rank-nullity theorem, or the definition of the rank as the dimension of the column space or row space of the matrix.

The rank of a matrix is always less than or equal to the number of its columns and rows, and it is equal to the minimum number of columns or rows that span the entire space.