Correct Answer - Option 1 : orthogonal
Explanation:
"λ" is called eigen value and "X" is called eigen vector of a square matrix "A", if
AX = λX
(i) Eigen values of a real symmetric matrix are always real.
(ii) Eigen vectors of a symmetric matrix corresponding to different eigenvalues are orthogonal to each other.
(iii) Sum of the eigen values of a matrix is always equal to the trace(sum of diagonal elements) of a matrix.
(iv) Eigen values of a matrix and its transpose are the same because the transpose matrix will also have the same characteristic equation.
Characteristics of eigen values:
- Tr (A) = Summation of eigen values
- |A| = Product of eigen values
- If A = Upper triangular matrix or lower triangular matrix or diagonal matrix, then its eigen values will be diagonal elements.
- Eigen values of the hermitian matrix and real symmetric matrix are always real.
- Eigen values of skew symmetric and skew hermitian matrix are either zero or purely imaginary.
- Eigen values of the orthogonal matrix and unitary matrix have unit modulus.
