Matrix Theory Quiz

The number of positive terms in the canonical form is called

• Signature

• Index

• Quadratic form

• Positive definite

A homogeneous polynomial of second degree in any number of variables is

• Canonical form

• Quadratic form

• Orthogonal

• Diagonal form

The eigen values of an orthogonal matrix have the absolute value ______

• 0

• 1

• 2

• ±1

All the eigen values of a symmetric matrix with real elements are

• Distinct

• Real

• Equal

• Conjugate complex numbers

The eigen vectors corresponding to the distinct eigen values of a real symmetric matrix are

• Imaginary

• Non-orthogonal

• Real

• Orthogonal

The rank of the zero matrix of order 3×3 is

• 0

• 1

• 2

• 3

The trace of a square matrix is defined as

• Sum of diagonal elements

• Product of diagonal elements

• Determinant of the matrix

• Sum of all elements

Which of the following matrices is diagonalizable?

• Symmetric matrix

• Skew-symmetric matrix

• Non-square matrix

• Upper triangular matrix with repeated eigenvalues

If a matrix is both upper and lower triangular, then it must be

• Identity matrix

• Diagonal matrix

• Zero matrix

• Symmetric matrix

The characteristic polynomial of a matrix is used to find its

• Rank

• Determinant

• Eigen vectors

• Eigen values