The definition of matrix rank is the number of vectors contained in the largest independent group of its row vectors or column vectors.

The fundamental reason for this definition is that the row rank and column rank of a matrix are equal (it is proved that n+ 1 n-dimensional vectors can be linearly correlated).

The geometric meaning of the rank of matrix is as follows: by defining linear transformation in n-dimensional linear space v, it can be proved that any linear transformation can correspond to an n-order matrix one by one under a given set of bases; But also keep linearity; In other words, the space composed of all linear transformations is over.

Extended data:

The maximum order of a non-zero subformula with A=(aij)m×n is called the rAnk of matrix A, and it is denoted as ra, or rankA or R(A).

In particular, it is stipulated that the rank of zero matrix is zero.

Obviously, rA≤min(m, n) can be easily obtained: If at least one R-order sub-formula in A is not equal to zero, and in R.