# Tagged Questions

Questions about Mathematica functionality related to manipulating vector spaces and linear mappings between such spaces. This includes determination of matrix properties, matrix transformations, decompositions, and factoring.

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### Solving for five unknowns in a 3 x 3 matrix

I know that matrix.Transpose[matrix] = IdentityMatrix[3] matrix = {{0.8111, 0.4867, -0.3244}, {a,b,0}, {c,d,e}} I tried ...
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### Speedup matrix number multiplication

Consider this simple matrix number multiplication: ...
869 views

### How to simulate the response of a linear parametric varying system in Mathematica?

Consider the following system \begin{align} \dot{x}(t)&=\sum_{i=1}^{2}\rho_{i}(x(t))\left[A_{i}x(t)+B_{i}u(t)\right]\\ y(t)&=Cx(t) \end{align} with: ...
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### Finding an Integer, Unimodular Matrix that connects two given matrices

I have two symmetric, integer matrices, $K$ and $K_2$ which have the same determinant and the same signature (number of positive - number of negative eigenvalues). I want to find an integer valued ...
841 views

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### Hash in Eigenvalue calculation [duplicate]

When I tried to find the eigenvalue of a 5x5 matrix, I get the following ...
95 views

### Sum to Zero Constraint in GeneralizedLinearModelFit

Is there a way to impose a constraint on a generalized linear model fit in Mathematica? In R, when using the glm() function, you can set options(contrasts=c('YY.sum', 'ZZ.sum')). Is there something ...
45 views

### Getting the row/column reduction matrix of a matrix m

Is there a simple way to get the row reduction matrix for a matrix m? As in, a matrix a such that ...
68 views

### Unexpected behavior from applying ToRadicals to eigenvalues [closed]

I am trying to get the symbolic form of a $10 \times 10$ matrix (I know, that is generally too large). ...
87 views

### Real Canonical Form of Arbitrary Size Matrices

I have been searching the site and the Mathematica documentation, but have not found anything regarding this. If we find the Jordan Form of the following matrix, we get complex values, but I would ...
64 views

### Trouble implementing logarithmic matrix norm

I wanted to write a quick function that calculates the logarithmic matrix norm with respect to the spectral norm. The formula is $$\mu_2(A) = \lambda_\mathrm{max}\left(\frac{A + A^T}2\right).$$ So ...
103 views

### Find partial solution for underdetermined system of Boolean equations (Minesweeper)

In this article about creating a Minesweeper solver, the author talks about using matrices to solve given portions of a Minesweeper board. While reading that, I thought of a different way to limit the ...
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### Plotting eigenvalues smoothly

I am trying to plot how the eigenvalues of a matrix change by changing a given a parameter t. Of course the ordering of the eigenvalues does not matter mathematically but it does when I want to make ...
58 views

### Strange sharp spikes causing overflow while doing gradient descent

I am trying to find a function h(r) that minimises a functional H(h) by gradient descent. The result of H(h) is a single number. (Basically, I have a field configuration in space and I am trying to ...
72 views

### Symbolic calculation of the rank of jacobian matrix

I would like to symbolically determine the rank of a jacobian matrix. In the help, I have seen that the MatrixRank function can be used for this purpose. However, when I use this function, the ...
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### Creating a transformation matrix with respect to given bases? [closed]

Let's say I have a linear transformation $T:V\to W$, along with some bases $\{v_1,v_2\}$ and $\{w_1,w_2,w_3\}$ of each respectively. Let's say all the information I have about the transformation and ...
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### Efficiently Invert a Square, Block Diagonal Matrix

I am generating an n x n matrix where n is specified by DIM: ...
158 views

### Bug in PositiveDefiniteMatrixQ?

Fixed in 10.1.0. Exists in at least 9.0.1 -- 10.0.2. This seems like a bug in PositiveDefiniteMatrixQ to me: ...
268 views

### LinearSolve and Krylov Method options

I need to solve a large, sparse, linear system. At some point Method -> "Multifrontal" fails and a bit later also "Pardiso" ...
104 views

### linear system equation ( trying to solve ) [closed]

I am trying to solve this system 3.7 x1+51.5 x10+71.3 x11-84. x2-16. x3-57.7 x4+89.7 x5-54.9 x6-85.8 x7+57.8 x8-51.3 x9==-36.8 -86.3 x1+5.7 x10-0.2 x11-39.9 x2+52.6 x3-45.6 x4+78. x5+90.7 x6-86.2 x7-...
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### Higher order SVD

Does anyone know how to do a higher order SVD in Mathematica ? A good reference seems to be here http://www.sandia.gov/~tgkolda/pubs/pubfiles/SAND2007-6702.pdf but I don't understand their formalism ...
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### Extract solutions of linear system to variables

I need to output the answers from solve into the variables named just as they were named in the solve equations. I have checked out this thread Assign the results from a Solve to variable(s) but ...
251 views

### Why is Mathematica eating a row from QRDecompostion

I'm attempting to calculate the QRDecomposition of the matrix: a = {{1, 3}, {0, 5}, {2, -8}} QRDecomposition[a] The answer ...