# 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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### How to find other basis of polynomials of degree three or less?

How can i find a basis of polynomials of degree three or less, which is other than $\{1,t,t^2,t^3\}$ ?
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### $s_j(A)=1$ for all $j$ iff $A^*=A^*AA^*$ and $A=AA^*A$

I want to show that all the non-zero s-numbers, i.e. singular values $s_j(A):=(\lambda_j(A^*A))^{1/2}$, of A (a bounded linear operator of finite rank acting on a separable Hilbert space $H$) are ...
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### Existence of a basis $B$ such that $M(\phi,B)=E$

Considering the matrix $$A=\begin{bmatrix}{2}&{1}&{0}\\{1}&{0}&{-1}\\{0}&{-1}&{-2}\end{bmatrix}\in M_3(R).$$ And $\phi:R^3 \times R^3\longrightarrow R$ the bilinear ...