Orthogonal Complements of Null Spaces of Matrices and their Transposes

We consider the relationships between null spaces and images of matrices and the orthogonal complement of their transposes. The structure of the inner product and transpose operators allows us to characterize the orthogonal complement of null spaces and images in terms of the images and null spaces of the transpose respectively. We use the fact that the orthogonal complement and transpose are involutions on finite dimensional spaces.
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[@volkandemir6353]

Thanks for videos Sir. I newly saw your channel and it is amazing. Can you write the name of the books that you are following for that playlist to description of playlist. Which book do you use for linear algebra?

[@mikethemathematician]

@volkandemir6353 Thanks for watching! I use my own notes, but I reference Linear Algebra Done Right by Axler and Linear Algebra Done Wrong by Treil!