Consider the linear space of all matrices for which all the vectors are eigenvectors. Describe the space (the matrices in "have a name"), and determine the dimension of .
Hence, the required dimension is n .
Eigenvectors are a nonzero vector that is mapped by a given linear transformation of a vector space onto a vector that is the product of a scalar multiplied by the original vector.
Let’s consider the linear space or all matrices which all the vectors role="math" localid="1659528394250" are Eigen vectors.
We want to describe the space and determine its dimension.
The set of matrices in the space spanned by the Eigen vectors are called diagonal matrices.
If you put all the vectors together in one large matrix it will have only values across the diagonal, thus the name diagonal matrix.
Since all Eigen vectors span the space and are linearly independent.
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