Answer by M. Van for Determinant of a rank $1$ update of a scalar matrix, or...
Here’s an answer without using eigenvalues: the rank of $A$ is $1$ so its image is spanned by some nonzero vector $v$. Let $\mu$ be such that$$Av=\mu v.$$We can extend this vector $v$ to a basis of...
View ArticleAnswer by Marc van Leeuwen for Determinant of a rank $1$ update of a scalar...
The formulation in terms of the characteristic polynomial leads immediately to an easy answer. For once one uses knowledge about the eigenvalues to find the characteristic polynomial instead of the...
View ArticleDeterminant of a rank $1$ update of a scalar matrix, or characteristic...
This question aims to create an "abstract duplicate" of numerous questions that ask about determinants of specific matrices (I may have missed a few):Characteristic polynomial of a matrix of...
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