- #1
ZedCar
- 354
- 1
Homework Statement
1x2 Matrix A =
[(5) (-2i)]
What is the complex conjugate and Hermitian conjugate of this matrix?
Homework Equations
The Attempt at a Solution
D^T =
5
-2i
D^H =
5
+2i
What do you think of my answers?
ZedCar said:Homework Statement
1x2 Matrix A =
[(5) (-2i)]
What is the complex conjugate and Hermitian conjugate of this matrix?
Homework Equations
The Attempt at a Solution
D^T =
5
-2i
D^H =
5
+2i
What do you think of my answers?
A complex conjugate of a matrix is a matrix with the same elements as the original matrix, but with the imaginary components of each element multiplied by -1.
A Hermitian conjugate of a matrix is a matrix with the same elements as the original matrix, but with the complex conjugate of each element in the transposed matrix.
To find the complex conjugate of a matrix, simply multiply the imaginary components of each element by -1.
To find the Hermitian conjugate of a matrix, first transpose the matrix and then take the complex conjugate of each element in the transposed matrix.
Complex and Hermitian conjugates are important in matrix operations because they allow us to perform operations such as multiplication and inversion on complex matrices and maintain the properties of the original matrix, such as symmetry and orthogonality.