Questions tagged [matrices]
For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate and adjoint, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), invariant factors, quadratic forms, etc. For questions specifically concerning matrix equations, use the (matrix-equations) tag.
5 questions from the last 7 days
2
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1
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115
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Finding inverse of a $3 \times 3$ matrix with Cayley-Hamilton, and Diophantine equation
I am trying to use this formula to find the inverse of a $3 \times 3$ matrix.
$$ \mathbf A^{-1} = \frac{1}{\det(\mathbf A)} \sum_{s=0}^{n-1}\mathbf A^{s} \sum_{k_{1}, k_{2},\dots,k_{n-1}} \prod_{l=1}^{...
- 23
1
vote
2
answers
200
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How to symbolically find inverses of matrices? [duplicate]
Today I met the following problem.$\newcommand\b\boldsymbol$
If $\b A$, $\b B$, $\b A+\b B\in\Bbb R^{n\times n}$ are non-singular matrices, find the inverse of $\b A^{-1}+\b B^{-1}$.
The solution is ...
- 5,070
0
votes
1
answer
39
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Matrices that are related to their transpose via diagonalizable matrices
I'm currently working with matrices having the following property:
Let $A \in M_n(\mathbb Z)$ be square matrix such that there exist diagonalizable matrices $S,T \in M_n(\mathbb C)$ with $A = S A^t T$,...
- 197
-6
votes
0
answers
39
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The Imitation Number Formula in the Collatz Conjecture is it novel [closed]
I have been analysing the Collatz Conjecture and have identified an infinite family of numbers, which I call 'Imitation Numbers' (N), that share an identical initial trajectory structure with a ...
-1
votes
0
answers
24
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Graphs where nodes are connected but distant [closed]
Is it possible to make a graph consisting of 2n nodes such that every node is connected to every other node in at least n steps except n of the other nodes?
For example with 1, we make the graph with ...
- 45