6.6 Flashcards
1
Q
When is a matrix A diagonally dominant?
A
When the entry on the main diagonal is larger then the sum of all the magnitudes for the current row
2
Q
When is a matrix A strictly diagonally dominant?
A
When it as also non singular
3
Q
What are the advantages of a strictly diagonally dominant matrix?
A
GE can be performed without row or column interchanges, meaning there is not pivoting required and we can perform LU factorization with no P matrix
4
Q
A matrix is _________ if A^T = A
A
symmetric
5
Q
When is a symmetric matrix A positive definite?
A
When x^T Ax > 0 for every non-zero vector x
6
Q
How can you determine whether a symmetric matrix is SPD?
A
With determinants or arithmetic
