What does the matrix asterisk mean?

There is an asterisk in the upper right corner of the matrix: it is called adjoint matrix.

When the matrix A is invertible, the original matrix, the inverse matrix and the adjoint matrix satisfy the relationship.

AA* = |A|E

Multiply both sides by a- 1.

A * = | A | A- 1 In extended data linear algebra, is the adjoint matrix of a square matrix a concept similar to the inverse matrix? . If a two-dimensional matrix is reversible, then its inverse matrix and its adjoint matrix have only one coefficient difference, and this rule also exists for multi-dimensional matrices. However, the adjoint matrix also defines an irreversible matrix and does not need division.

Adjoint matrix formula: AA*=A*A=|A|E

When the rank of A is n, A is reversible and A* is reversible, so the rank of A* is n; When the rank of A is n- 1, according to the definition of rank, A has an n- 1 order cofactor that is not 0, so A* is not equal to 0. Moreover, according to the above formula AA*=0 and the rank of A is less than n- 1, it is known that any n- 1 order cofactor of A is 0 and A*.