Test 1 Flashcards
If x is an eigenvector of A, does Ax point in the same direction as x?
True – Ax = λx means x is only scaled, not rotated.
If C is a covariance matrix, then C’ = C.
True – Covariance matrices are always symmetric.
If R is a correlation matrix, then R is always invertible.
False – If two variables are perfectly correlated, the determinant is 0, making R singular (non-invertible).
If I is the n × n identity matrix, its trace is n.
True – The trace is the sum of diagonal elements, all of which are 1.
A covariance matrix could possibly be diagonal.
True – If all variables are uncorrelated, the off-diagonal elements are 0, making it diagonal.
For any square matrices A and B, does AB = BA?
False – Matrix multiplication is generally not commutative.
If a T²-test is significant for multivariate data, at least one univariate t-test on the same data must be significant.
False – The combined effect across multiple variables can be significant even if individual tests are not.
If all univariate t-tests are significant, must the multivariate T²-test be significant?
False – If variables are highly correlated, T² may not be extreme.
Performing multiple univariate t-tests increases the likelihood of a Type I error compared to a single t-test.
True – The probability of at least one false positive increases as more tests are performed.
Distance between two points is always non-negative.
True – By definition, a distance cannot be negative.
Euclidean distance does not account for relationships between variables.
True – It treats all dimensions independently, unlike Mahalanobis distance, which considers covariance.
what do you interpret distances with the project distance formula?
0 < x < 1. 1 being the most dissimilar and 0 being the most similar
