As said in the title, in which cases an invertible matrix is equal to the transpose? When is this: $ A^{-1} = A^{T} $ true?
If the matrix A is orthogonal?
Thank you!
As said in the title, in which cases an invertible matrix is equal to the transpose? When is this: $ A^{-1} = A^{T} $ true?
If the matrix A is orthogonal?
Thank you!
If $A^{-1}=A^T$, then $A^TA=I$. This means that each column has unit length and is perpendicular to every other column. That means it is an orthonormal matrix.
You're right. This is the definition of orthogonal matrix.