# Tagged Questions

Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc. For questions specifically ...

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### Assuming a ray defined by a starting point and a direction. How can I tell if a plane is behind it or in front of it?

If I have a ray defined by a starting point and a direction, and a plane defined by its normal and its distance from the origin, how can I tell if the plane is in front versus behind the ray? By ...
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### 3 x 3 linear system organization [duplicate]

How to organize this 3x3 linear system in order to solve it with determinants afterwards.
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### Finding maximum no of $1$'s

We are given a matrix $A \in M_n (F)$ such that all its entires are either $1$ or $0$. I need to find the maximum number of $1$'s that can be in matrix $A$ so that it is still invertible. My try : ...
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### Searching for analytical or topological proof(s) of the Cayley-Hamilton theorem

Is there any analytical or topological proof(s) of the Cayley-Hamilton theorem ? I want to know such proofs ( if possible ) , I would even appreciate proper references with accessible links . Thanks ...
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### Dimension of vector space of 2x2 skew symmetric matrices

I had a question about the dimension of this subspace. This was related to a problem that had a case of n x n matrices, but I accidentally read it as the special case of 2x2, but never the less the ...
I would like to invert a square matrix $L$. One can write it as a sum of two matrices, one containing the diagonal terms ($D$) and the other the off-diagonal ones ($A$). $$L = D+A$$ I would like ...