Px153 Revision Flashcards
How can you tell if a matrix has an inverse?
If the determinant is non zero it has an inverse
What are the requirements for convergence in the mean to occur?
Only that integral (f(x))² dx over the interval is less than infinity
When does piecewise convergence occur?
When the function is continuous over the interval except for a finite number of points, essentially there are breaks in the function
When does uniform convergence occur?
When the function is continuous over the interval and at periodic extensions
What matrices can be expressed in LU decompositions?
All square, non singular matrices
What is a hermitian matrix?
One where the values on the main diagonal (bottom left to top right) are complex conjugates of each other
What is a unitary matrix?
One where the inverse is equal to it’s hermitian (conjugate transpose) or the matrix multiplied by it’s hermitian is equal to the identity matrix
What is an orthogonal matrix?
One where it’s transpose is equal to it’s inverse
What is an antisymmetric matrix?
One where the negative is equal to the transpose of the original matrix
