# Matrix (mathematics): Quiz

Question 1: However, the explicit point of view of matrices tends to obfuscate the matter,[nb 3] and the abstract and more powerful tools of ________ can be used instead.
Linear algebraDynamical systems theoryFunctional analysisHilbert space

Question 2: Allowing as input two different vectors instead yields the ________ associated to A:

Question 3:  General groups can be studied using matrix groups, which are comparatively well-understood, by means of ________.
Lie groupGroup representationRepresentation theoryGroup (mathematics)

Question 4: Stochastic matrices are used to define ________ with finitely many states.
Eigenvalue, eigenvector and eigenspaceMarkov chainInformation theoryEntropy (information theory)

Question 5: [nb 2] Since in a group every element has to be invertible, the most general matrix groups are the groups of all invertible matrices of a given size, called the ________.
Special unitary groupLorentz groupGeneral linear groupOrthogonal group

Question 6: By the spectral theorem, real symmetric matrices and complex Hermitian matrices have an ________; i.e., every vector is expressible as a linear combination of eigenvectors.
Eigenvalue, eigenvector and eigenspaceVector spaceLinear algebraMatrix (mathematics)

Question 7: Besides the ordinary matrix multiplication just described, there exist other less frequently used operations on matrices that can be considered forms of multiplication, such as the Hadamard product and the ________.
Matrix (mathematics)Kronecker productSimilar matrixInvertible matrix

Question 8: Linear transformations and the associated ________ play a key role in modern physics.
Symmetry (physics)Group (mathematics)Euclidean groupSymmetry

Question 9:  These concepts can be applied to websites connected ________ or cities connected by roads etc., in which case (unless the road network is extremely dense) the matrices tend to be sparse, i.e.

Question 10: If only all entries above (below) the main diagonal are zero, A is called a lower ________ (upper triangular matrix, respectively).
Triangular matrixDeterminantMatrix (mathematics)Diagonalizable matrix