Rank = # of non-zero eigenvalues of a diagonalizable matrix
102166
What is the relation between rank of a matrix, its eigenvalues and eigenvectors
97040
Question about an application of the Rank-Nullity theorem
53993
Can Eigenvalues[] and Eigenvectors[] be assumed to return the same ordering?
58476
Why can a matrix whose kth power is I be diagonalized?
29788
Eigenvalues of a matrix whose square equals its transpose
125569
Prove that the eigenvalues of a real symmetric matrix are real
155451
Upper bound for the rank of a nilpotent matrix , if $A^2 \ne 0$
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
56083
Find the eigenvalues of a projection operator
112900
Eigenvalue of a polynomial evaluated in a operator
90576
Symmetric matrix eigenvalues
123679
General Information about Eigenvalues for an 3x3 symmetric matrix
898
Strictly diagonally dominant matrices are non singular
57296
A non-diagonal $4\times4$ matrix such that $A^3=A^2=0$ and its rank is $2$
110271
Given a matrix with non-negative real entries, can you algebraically prove that it has a non-negative eigenvalue?
135420
Determining eigenvalues, eigenvectors of $A\in \mathbb{R}^{n\times n}(n\geq 2)$.
82688
Least rank of a matrix