Hermitian and skew hermitian matrix

Express A as the sum of a Hermitian and a skew-Hermitian matrix, where A=[(2+3i, 2, 5), (-3-i, 7, 3-i), (3-2i, i, 2+i)]dot

Express A as the sum of a Hermitian and a skew-Hermitian matrix, where A=[(2+3i, 2, 5), (-3-i, 7, 3-i), (3-2i, i, 2+i)]dot

Which of the following is incorrect? 1. Determinant of Nilpotent matrix is 0 2. Determinant of an Orthogonal matrix = 1 or -1 3. Determinant of a Skew - symmetric matrix is 0. 4. Determinant of Hermitian matrix is purely real.

If A=[[1,2-3i,3+4i],[2+3i,0,4-5i],[3-4i,4+5i,2]] ,then A is (A) symmetric (B) Skew - symmetric (C) hermitian (D) Skew - hermitian

Show that every square matrix A can be uniquely expressed as P+i Q ,where P and Q are Hermitian matrices.

Show that every square matrix A can be uniquely expressed as P+i Q ,where P and Q are Hermitian matrices.

Show that every square matrix A can be uniquely expressed as P+i Q ,w h e r ePa n dQ are Hermitian matrices.

Show that every square matrix A can be uniquely expressed as P+i Q ,w h e r ePa n dQ are Hermitian matrices.

If A=[(1,2-3i,3+4i),(2+3i,0,4-5i),(3-4i,4+5i,2)] , then show that A is hermitian matrix.

…….. Matrix is both symmetric and skew symmetric matrix .