matrix

Operations of Matrix

Transpose

and

Conjugate transpose

Determinant

Properties of Matrix

Rank

• The rank of a matrix is equal to the number of non-zero rows if it is in Echelon Form.

Types of Matrix

• Singular, . It’s inverse is not exists.
• Diagonal, .
• Tridiagonal, .
• Triangular, lower: ; higher: .
• Symmetric, .
• Skew-Symmetric, .
• Hermitian, .
• Unitary, .
• Normal ; .
• Defective, Multiplicity with fewer than linearly independent corresponding Eigenvectors.
• Nondefective / diagonalizable, it has where is Eigenvectors.

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• Orthogonal matrix, .
• Symmetric positive definite matrix (SPD)
• Band matrix
• Vandermonde matrix
• Hessenberg matrix
• Jacobian matrix
• Hessian matrix