Chapter 1 & 2 Flashcards
What is a diagonal matrix?
A square (n=p) matrix which has zero-elements on the off-diagonal.
How do we denote the identity matrix for p = columns?
I_p.
What are the unit and the null matrices?
Matrices which contains only ones; and contains zeros for all elements, respectively.
What is the rank of a null matrix?
Zero.
How do we know when to look at rows or columns to examine rank of matrix?
Choose rows if rows are fewer than columns; columns if columns are fewer than rows. If rows = columns, the matrix has full rank either when its rows or its columns are linearly independent.
Which two assumptions need to be fulfilled for a matrix to be invertible?
1) Square and 2) needs to be invertible (non-singular = determinant = non-zero).
For a 3x3 matrix, we need XXX individual determinants to calculate the determinant of the full matrix?
Three.
What is the trace of a matrix?
The sum of its diagonal elements.
What happens when we take the transpose of a matrix multiplication (AB)’?
We need to shift A and B when “multiplying in” the transpose –> B’ A’.
What is the transpose of the transpose of a matrix A (A’)’?
A itself.
What is the benefit of standardizing variables?
That each variable will contribute equally to the variation and hence will be more fairly comparable, regardless of their respective scale.
How do the covariance and correlation matrices relate to unstandardized and standardized variables?
The correlation is just the standardized covariance. Hence, the covariance matrix of a standardized variable will equal the correlation matrix.
What are the dimensions of the sample variance-covariance matrix?
p x p, where p are the number of variables.
How many variances and covariances respectively does a variance-covariance matrix include?
p variances and 1/2 p (p-1) covariances.
What is the generalized sample variance?
The determinant of S, |S|.
