Topic 6 - Matrix Applications Flashcards
What does it mean that matrix is singular?
How do you find out if a matrix is singular?
A singular matrix does not have a inverse.
If the determinant of a matrix is 0, it is singular.
What do you need to remember about substraction or addition in the guassian elimination process?
Make sure you subtract down columns only. You can’t subtract a value in one column from another. They need to be in the same column.
What sort of matrix is this?
Identity Matrix / Unit Matrix
All diagonal elements are 1 and all non-diagonal elements are 0.
What sort of matrix is this?
Upper triangular matrix
What sort of matrix is this?
Strictly Upper triangular
What sort of matrix is this?
Symmetric Matrix
How is the transpose found again?
Found by exchanging the rows with the columns.
What sort of matrix is this?
Anti-symmetric or Skew-symmetric
When the matrix is equal to the negative of the tranpose. This requires the middle diagonal to be zero (diagonal element zero).
What sort of matrix is this?
Hermitian matrix
A matrix is Hermitian when the tranpose of the conjugate of that matrix is equal to the original matrix.
What is a anti-hermitian or skew hermitian matrix?
This is when the matrix is equal to the negative of its conjugate transpose (i.e. the transpose of its conjugate).
. AH = -A, noting that this requires the diagonal elements to be zero
What is a Orthonormal or Orthogonal Matrix?
The product of the matrix with its transpose is equal to the identity matrix. i.e. ATA = A AT = I
What do you call it when the number of number of independent equations is equal to the number of unknowns and the equations are consistent?
The system is uniquely determined.
What do you call it when number of independent equations is less than the number of unknowns and the equations are consistent?
i.e. the number of equations is less than the unkowns
The system is underdetermined.
A non-unique solution is possible
What do you call it when independent equations is less than or equal to the number of unknowns and the equations are inconsistent?
No solution is possible.
What do you call it when the number of independent equations is greater than the number of unknowns, those equations cannot be consistent?
There is no solution. The system is overdetermined.
What does consistency mean in simultaneous equations?
What does it mean when a set of equations is inconsistent?
If any equations contradict each other. These equations are inconsistent
Solve the system of simultaneous equations using standard Gaussian elimination.
No unique solution as underdetermined.
Determine the eigenvalues of this matrix.
