linearly independent in a sentence

Examples

1. The JHF will be diagonal if and only if you have " p " linearly independent eigenvectors.
2. Consider a general situation where we have n underlying assets and a linearly independent set of m Wiener processes.
3. And would they be linearly independent ? ) talk ) 15 : 50, 3 December 2008 ( UTC)
4. A basis is just a linearly independent " set " of vectors with or without a given ordering.
5. Since S is linearly independent and T spans, we can apply Theorem 1 to get m \ geq n.
6. Consequently, there will be three linearly independent generalized eigenvectors; one each of ranks 3, 2 and 1.
7. This is the unique least-squares solution as long as \ mathbf { X } has linearly independent columns.
8. The article on the Wronskian gives an example of two examples that are linearly independent with a Wronskian of zero.
9. In this example the " 3 miles north " vector and the " 4 miles east " vector are linearly independent.
10. Okay if they're not that doesn't help us at all in showing anything about linearly independent vectors.