# 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.

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### What problems will arise if we define matrix multiplication this way?

$a\in \mathbb{R}^n$ $a=(a_1,a_2,\dots,a_n)$ lets define this to be equivalent to $(a_1,a_2,\dots,a_n,0,0,0 \dots,0)$ (finite many zeros) by this I think we can make an $n \times m$ matrix $A$ ...
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### Simultaneous diagonalisation of quadratic forms

Is there a linear transformation that simultaneously reduces the pair of real quadratic forms $$x^2-y^2$$ and $$2xy$$ to diagonal forms? My attempt I know that neither of these forms are positive ...
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### Diagonalization/Eigenvalues of block matrices

Suppose I have two square $2^n \times 2^n$ matrices $A$ and $B$. Suppose furthermore that $A$ and $B$ are both symmetric matrices with real coefficients. Therefore their eigenvectors can be chosen to ...
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### Gram schmidt swapping two vectors

The question has background here but it's really just a linear algebra question. Suppose I have $B = (b_1,\cdots,b_n)$ vectors and I perform Gram Schmidt process (with no normalization of vector) ...