The necessary and sufficient condition of linear correlation can be that the value of determinant is equal to 0? The necessary and sufficient condition of linear independence can be that the value of determinant is not equal to 0? Is the above statement correct?

The necessary and sufficient condition of linear correlation can be that the value of determinant is equal to 0? The necessary and sufficient condition of linear independence can be that the value of determinant is not equal to 0? Is the above statement correct?


When the number of vectors is equal to the dimension of vectors, the above conclusion holds



A necessary and sufficient condition for determinant a to be greater than or equal to 0
For example, | a 20|
| 2 a 0 |
|What is the necessary and sufficient condition for this determinant to be greater than or equal to zero? How to calculate it,


a> A = 2 or a = 0