Different matrix forms have their own advantages, and there are significant differences in definition, form and expressive ability. In this paper, the characteristics and application scenarios of three matrix forms, namely, row simplest form, ladder form and row ladder form, will be discussed in depth to help readers better understand.

Row simplest matrix

The simplest row matrix requires that the first element of each row must be 1, and the whole matrix is in the form of rules. It can clearly represent the row transformation and elimination operations of the matrix, thus facilitating our further calculation and analysis.

Trapezoidal matrix

Trapezoidal matrix requires that the first non-zero element in a non-zero row is all 1, and all other elements in the column where this element is located must be all zeros. It is more like a ladder, each ladder has only one row, and the other elements after the first element of the non-zero row can be arbitrary values. It can display the position and distribution of non-zero elements in the matrix more intuitively, which is convenient for us to understand the structure of the whole matrix.

Row trapezoid matrix

The characteristic of row ladder matrix is that its non-zero elements are arranged like steps, and there is only one row in each step. The subscript of the column where the first non-zero element of non-zero row is located increases strictly with the increase of row label. It can clearly represent the row transformation and elimination operations of the matrix, thus facilitating our further calculation and analysis.