# Questions tagged [matrix-rank]

For questions regarding the rank of matrices in linear algebra.

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### If $A$ and $B$ are normal with $\sigma(A),\sigma(B)\subseteq \mathbb{R}\cup\mathbb{T}$, does $\text{dim ker}(AB-BA)=\text{dim ker}(A^*B-BA^*)$?

I already asked this question for general $B$ and it was answered negatively here, so if the statement is true, one has to use the assumption on $B$ as well. In the original question I already ...
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### Finding rank of matrix $A$.

Let $A_{n×n}$ =$((a_{ij}))$ n≥3 , where $a_{ij}=(b_i^2−b_j^2)$ , i,j=1,2,…,n for some distinct real numbers $b_1,b_2,…,b_n$ . Then what is $\rho (A)$ ? My attempt: A can be written as difference of ...
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### Rank and Nullity of Matrix with Arbitrary Parameters

Given the matrix A defined as A = \begin{bmatrix} 2 & -4 & 4 & -2 \\ 6 & a-2 & 7 & a-6 \\ -1 & 2-b & 8 & -b+1 \\ \end{bmatrix} where (a) and (b) are real constants, ...
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### Can anyone help with this matrix problem? [duplicate]

enter image description here In this image, there's a question about asking to get the determinant of matrix D. I'm stuck on how to represent it as using only a and n.
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