Matrix and Eigenvalues Quiz

What is an Eigenvalue of a matrix?

• A type of matrix

• A number that stretches a vector

• A column of numbers

• A row of numbers

What do we call a matrix that is similar to a diagonal matrix?

• Block matrix

• Identity matrix

• Square matrix

• Diagonalizable matrix

What is the characteristic polynomial of a matrix?

• A vector

• A polynomial that helps find Eigenvalues

• A type of matrix

• A number

What does the Cayley-Hamilton theorem state?

• Every matrix is a root of its characteristic polynomial

• All matrices are similar

• Matrices cannot be diagonalized

• Eigenvalues are always positive

What is an Eigenvector?

• A vector that does not change direction when multiplied by a matrix

• A type of matrix

• A polynomial

• A number

What is the minimal polynomial of a matrix?

• The polynomial of least degree that has the matrix as a root

• A vector

• A type of matrix

• A number

What is a decomposable matrix?

• A vector

• A matrix similar to a block diagonal matrix

• A type of matrix

• A number

What is the spectral radius of a matrix?

• The largest magnitude of its Eigenvalues

• A type of matrix

• A vector

• A number

What is the purpose of diagonalization?

• To multiply matrices

• To find the sum of matrices

• To create new matrices

• To simplify matrix calculations

What does it mean for two matrices to be similar?

• They have the same size

• They can be transformed into each other by an invertible matrix

• They are the same matrix

• They have the same numbers