# Tagged Questions

For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), ...

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### How can two vectors, with three elements each, form a base of a two dimensional space?

I might have misunderstood something(most likely the case), but there's an example. Assume this matrix: $\begin{bmatrix} 1& 2&3 \\ 1& 1& 2\\ 1& 2 &3 \end{bmatrix}$ ...
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### Given det(A) = 2. Find the Determinant of this Matrix

I've run into a roadblock that my textbook doesn't seem to be able to help me with. I am not understanding how to solve these type of questions. I am assuming to receive the answer given, you do some ...
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### Recursive matrix multiplication strassen algorithm

I am having a hard time doing 4x4 matrix multiplication using strassen's algorithm. First I computed the product of two 4x4 matrices using default matrix multiplication (https://matrixcalc.org) I ...
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### Solve linear system with $A_{i,j} = \langle e_i, e_j\rangle^2$, edges of a triangle

I have three vectors in $e_i\in\mathbb{R}^3$ that form a triangle. Let us consider now the linear equation system $Ax=b$ with $$A_{i,j} = \langle e_i, e_j\rangle^2,\\ b_i = \langle e_i, e_i\rangle.$$...
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### Calculating probabilities in a Markov chain process

I have 3 variables A, B and C with each variable having a probability of 0.6 and 0.4 i.e. A can have states (ON) with probability of 0.6 as well as can remain in certain states (OFF) with probability ...
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### Prove an equality of complex matrixes

If $A \in M_2(\mathbb{C})$ a matrix so that $$\det\left(A^2 + A + I_2\right)=\det\left(A^2 - A + I_2\right)=3 \tag1$$ then $$A^2\left(A^2 + I_2\right)=2I_2. \tag2$$ I tried to use Cayley-Hamilton ...
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### About matrix diagonalization in C from the characteristic polynomial.

Ok the excercise is: You have one characteristic polynomial, it's: $\lambda^4 + \lambda^2$ Find two matrixes with this polynomial, one of them diagolalizable in C and the other one not. so the ...
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### Derivative of $X_u A X B X_u^T$ w.r.t. $X_u$

How to solve this $\frac{d X_u A X B X_u^T}{d X_u}$, where $X, A, B \in \mathbb{R}^{n \times n}$ and $X_u$ is the $u$-th row in $X$?
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### To distinguish among the various subsets of $M_n(\Bbb R)$

I am having problem in doing a certain type of problems relating to matrices: To distinguish among the various subsets of $M_n(\Bbb R)$ such as symmetric, diagonal, diagonalizable, upper triangular, ...
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### Prove that determinant of a 2x2 symmetric positive definite matrix is positive by “completing the square” method.

From my understanding, determinant = product of Eigen values. Since it is a positive definite matrix, the eigen values are positive and hence, the determinant is ...