Abstract
This chapter discusses special matrices, quadratic forms, differentiation of matrices, and the matrix exponential. Special matrices include diagonal matrix, identity matrix and null matrix, reducible and irreducible matrices, equivalent matrices, transpose of a matrix, adjoint matrix, inverse matrix, trace of a matrix, symmetric matrix, skew-symmetric matrix, triangular matrices, orthogonal matrices, Hermitian matrix, Unitary matrix, Nilpotent matrix, and Idempotent matrix. Under quadratic forms Sylvester's law of inertia is discussed with its rank, signature, and positive definite and semidefinite quadratic form. In addition, the basic properties of matrix exponential are explained.
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