Matrix A-type N-orderreversible matricesThe equivalent conditions:
1. A'sdeterminant not equal to 0
2. A'srank equals n, that is, A isFull RankMatrix
3. Row of a (column)Vector Group Linear Independent
4. Homogeneous equation setax=0 only 0 Solutions
5. For any b belongs to RN (n is superscript, which represents vector space), ax=b always has a unique solution
6. A is equivalent to the unit matrix
7. A can be expressed as a product of several elementary matrices
8. The column vectors of a can be used as a set of bases for n-dimensional vector space Rn (n as superscript)
9. Any vector in Rn can be made up of a column vectorLinear meter out
10. A'sthe eigenvalues are not all 0 .
11. At A is a positive definite matrix (where T is superscript, which indicates the transpose of a)
12. A isnon-singularOf
Equivalent conditions of invertible matrices
