Citan Uzuki said:Yes. The determinant is a polynomial with real coefficients of the entries in A, and for any polynomial p in n variables with real coefficients, p(x_1*, x_2*, ... , x_n*) = p(x_1, x_2, ... , x_n)*.
The determinant of a complex matrix is a numerical value that is calculated from the entries of the matrix. It is used to determine certain properties of the matrix, such as whether it is invertible or singular.
The determinant of a complex matrix is calculated using a specific formula that involves the entries of the matrix. This formula can vary depending on the size of the matrix, but it typically involves multiplying and adding the entries in a specific way.
The determinant of a complex matrix represents the scaling factor of the matrix. This means that multiplying the matrix by a scalar value will also multiply the determinant by that same value. It can also be interpreted as the volume of the parallelepiped formed by the columns or rows of the matrix.
Yes, the determinant of a complex matrix can be negative. In fact, the sign of the determinant can provide information about the orientation of the coordinate system in which the matrix is represented.
The determinant of a complex matrix has various applications in mathematics, physics, and engineering. It is used to solve systems of linear equations, find inverses of matrices, and calculate areas and volumes in geometric problems. It is also used in machine learning, computer graphics, and quantum mechanics.