Section 1 Flashcards
What are conformable matrices?
Matrices of the right dimensions to be able to perform the operation required
What are the following:
a) Null matrix
b) Square matrix
c) Diagonal matrix
d) Identity matrix?
a) 0s in every element
b) matrix same no. of rows and columns
c) matrix with 0s everywhere except main diagonal
d) square matrix kxk, 1s on main diagonal, 0s elsewhere
What is a symmetric matrix?
When A=A’
What is a trace?
Sum of diagonal elements of A, denoted tr(A)
What is linear dependence?
When each element in a row or column is exactly related to those of other rows or columns
Difference between a singular and non-singular matrix?
A singular matrix has rows/columns that are linearly dependent
A non-singular matrix has no linearly dependent rows/columns
What is the rank of a matrix?
The number of linearly dependent rows/columns a matrix has
How are determinants denoted? (eg. matrix A)
|A| (check i can do aswell)
What is the adjoint?
Denoted adj(A) it is the transpose of the matrix of cofactors of A
What type of matrices are invertible?
Square, non-singular matrices
What is an idempotent matrix?
One that equals itself when multiplied by itself
AA=A
Quick way to see if a matrix is positive definite? and positive semi-definite?
If all LPM are positive
PSD if all LPM are non-negative
Quick way to see if a matrix is negative definite? and negative semi definite?
When all odd numbered LPM are negative and all even numbered are positive
NSD if all odd numbered LPM are negative or 0 and all even numbered are positive or 0
Expected value of a matrix?
=The expected value of each element (see notes end of S1!!!)
