I have noticed a matrix property that is outlined below:
I have a set of n orthonormal eigenvectors that form a basis in Rn. If these vectors are combined to form an nxn matrix where each column is one of the eigenvectors, the rows in this matrix are also normalized but not necessarily orthogonal to each other.
Can someone help me prove or disprove this?
On
It is a theorem of linear algebra that a set of $n$ $n$-dimensional column vectors form an orthonormal basis if and only if they satisfy $AA^T = I$ where $A^T$ is the transpose of the matrix and $A$ is the matrix where the basis vectors are the columns. It's also a theorem that $(A^T)^T = A$ and the inverse of a matrix is unique. So what can you say about the rows of $A$, assuming that the columns of $A$ are orthonormal?
It $M^T \times M = I$, what can you say about $M \times M^T$?