Maths - Matrix algebra - Transpose

This applies only to a square matrix, it means swaping the rows and columns.

In other words element mij becomes element mji

m00 m01 --> m10 m02 --> m20
m10 --> m01 m11 m12 --> m21
m20 --> m02 m21 --> m12 m22

The transpose of matrix M is normally denoted by Mt.

Conjugate transpose

U* = the conjugate transpose of U.

The conjugate transpose is also known as adjoint matrix, adjugate matrix, hermitian adjoint or hermitian transpose.

This only applies to a matrix whose elements are complex numbers, quaternions or octonions.

The conjugate matrix is the complex conjugate of each element.

The conjugate transpose is the conjugate matrix and the transpose of the matrix applied together.

 

 


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