Sciencemaster's latest activity
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Sciencemaster replied to the thread I How do Tensors "work" in relation to linear algebraic objects?.That's fair. I'm just trying to visualize what expanding a vector into "more dimensions" really 'looks' like. A tangent vector being... -
Sciencemaster replied to the thread I How do Tensors "work" in relation to linear algebraic objects?.First off, thanks for fixing my formatting. I knew about the curly brackets, I just missed them when I was typing. I keep getting...
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Sciencemaster posted the thread I How do Tensors "work" in relation to linear algebraic objects? in Special and General Relativity.I've been reviewing some introductory tensor stuff, and I've come to the realization that some of the things tensors do confuse me. For...
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Sciencemaster replied to the thread I How do non-diagonal indices of a metric allow for local flatness?.Alright. In that case, if local flatness just means that a metric's Christoffel symbols are 0 to first order (on a small enough scale)...
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Sciencemaster replied to the thread I How do non-diagonal indices of a metric allow for local flatness?.Fair enough. In that case, though, what exactly *does* locally flat/Minkowskian mean? It seems to me like the Minkowski metric can be...
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Sciencemaster replied to the thread I How do non-diagonal indices of a metric allow for local flatness?.Thank you, but I think I found them myself. When you get a chance (seriously, no rush), is this a copy of the right one...
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Sciencemaster posted the thread I How do non-diagonal indices of a metric allow for local flatness? in Special and General Relativity.I'm having trouble understanding the local flatness of GR. So far, my interpretation was that it meant that the metric tensor at an...
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Sciencemaster replied to the thread I Can one find a matrix that's 'unique' to a collection of eigenvectors?.I see. It makes more sense when I look at it like this: The columns of a matrix transformation represent where the standard basis...
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Sciencemaster replied to the thread I Can one find a matrix that's 'unique' to a collection of eigenvectors?.Alright, I think I’m starting to get how this works (also, thanks to pasmith who explained it like this). In short: yes — if you’re...
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Sciencemaster replied to the thread I Can one find a matrix that's 'unique' to a collection of eigenvectors?.I went back and checked, and they definitely do share eigenvalues. Double checking the math (and also doing the reverse calculation with...
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Sciencemaster replied to the thread I Can one find a matrix that's 'unique' to a collection of eigenvectors?.This is very helpful. One thought I had about the diagonal matrix is this: since the eigenvectors in the matrix #P# are aligned with the...
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Sciencemaster replied to the thread I Can one find a matrix that's 'unique' to a collection of eigenvectors?.Just to check, if a matrix has an inverse, that means that its transformation is necessarily one-to-one, right? Meaning, if we transform...
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Sciencemaster replied to the thread I Can one find a matrix that's 'unique' to a collection of eigenvectors?.I think I may be miscommunicating a little. For this specific example, what I'm trying to check for is whether...
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Sciencemaster replied to the thread I Can one find a matrix that's 'unique' to a collection of eigenvectors?.What I meant by 'general' is that we use scalar parameters like a and b in the place of indices in the final matrix, eigenvalues, etc. I...
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Sciencemaster replied to the thread I Can one find a matrix that's 'unique' to a collection of eigenvectors?.Are you sure? I'm pretty sure that ##\begin{bmatrix}1&4\\1&1\end{bmatrix}## has the eigenvectors ##\begin{bmatrix}2\\1\end{bmatrix}##...