Data Fundamentals (H) - Week 05 Quiz
1. Applying the linear map defined by the matrix \(A\) to the column vector \(\vec{x}\) should be written:
\(\vec{x}A\)
\(A\vec{x}^T\)
\(\vec{x}A\vec{x}^T\)
\(A\vec{x}\)
\(\vec{x}^TA\vec{x}\)
2. Repeatedly applying a matrix \(A\) to a random initial vector \(\vec{x}_0\), normalising after each step, will lead to:
the minor eigenvector
zero
the leading eigenvector
the cross eigenvector
infinity
3. If \(A\) is orthogonal, then:
\(A^{-1} = A^T\)
\(A = AA^T\)
\(A^T=A\)
\(A^A=T^A\)
\(A = A^{-1}\)
4. The adjacency matrix of an
undirected
graph is:
Circulant
Self-similar
Adiabatic
Non-singular
Symmetric
5. In a stochastic matrix:
all elements are either 0 or 1
the sum of all elements is 1
the sum of each row 0
the sum of all elements is -1
the sum of each row is 1
6. The determinant of a matrix is equal to:
The product of the rows
The sum of the diagonal
The sum of the eigenvalues
The Frobenious norm of the matrix
The product of the eigenvalues
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