List questions from numerical-linear-algebra

69

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Show $\Vert A\Vert_2 = \sup_{x \neq 0} \frac{x^T A x}{x^T x}$ where $A$ is symmetric and positive-definite

Published on 16 Apr 2026 - 0:12

917

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Explain every steps of the Modified Gram–Schmidt algorithm

Published on 11 May 2026 - 2:39

34

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Solving a system of Trignometric equations

Published on 10 Apr 2026 - 18:28

52

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Finding the solution $\xi$ of $(M + \xi)x = y$ with the smallest 2-norm.

Published on 14 Apr 2026 - 9:37

31

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Showing $\sup_{\Vert w \Vert_\infty} |v^\ast w| = \Vert v \Vert_1$ for $v \neq 0$

Published on 13 Apr 2026 - 16:28

91

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Show convergence of an algorithm within $m$ steps

Published on 15 Apr 2026 - 10:48

66

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Prove that $\lim_{k\rightarrow > \infty} \frac{\|A^{k+2}x\|}{\|A^{k}x\|}=\lambda^2$

Published on 16 Apr 2026 - 2:43

35

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Estimating rate of decay of residual norms in gradient descent

Published on 15 May 2026 - 4:15

79

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Gram-Schmidt: how close are resulting vectors to $0$?

Published on 14 Apr 2026 - 7:11

89

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Fitting parabola to data set using inner products

Published on 11 Apr 2026 - 4:36

51

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Solving for $L$, where $P_n \cdots P_1 = I - XLX^T$, with $\Vert x_i \Vert_2=1$, $P_i := I - 2x_i x_i^T$, $X=[x_1 \cdots x_n]$

Published on 16 Apr 2026 - 20:06

247

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Condition number growth with "column add" operation

Published on 11 Apr 2026 - 10:13

1.3k

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Computational cost of finding only the eigenvalues

Published on 09 Apr 2026 - 18:13

654

Views

convergence of unshifted $QR$ algorithm proof

Published on 15 Apr 2026 - 2:42

104

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What do these matrices converge to?

Published on 11 Apr 2026 - 8:01

List Question

Show $\Vert A\Vert_2 = \sup_{x \neq 0} \frac{x^T A x}{x^T x}$ where $A$ is symmetric and positive-definite

Explain every steps of the Modified Gram–Schmidt algorithm

Solving a system of Trignometric equations

Finding the solution $\xi$ of $(M + \xi)x = y$ with the smallest 2-norm.

Showing $\sup_{\Vert w \Vert_\infty} |v^\ast w| = \Vert v \Vert_1$ for $v \neq 0$

Show convergence of an algorithm within $m$ steps

Prove that $\lim_{k\rightarrow > \infty} \frac{\|A^{k+2}x\|}{\|A^{k}x\|}=\lambda^2$

Estimating rate of decay of residual norms in gradient descent

Gram-Schmidt: how close are resulting vectors to $0$?

Fitting parabola to data set using inner products

Solving for $L$, where $P_n \cdots P_1 = I - XLX^T$, with $\Vert x_i \Vert_2=1$, $P_i := I - 2x_i x_i^T$, $X=[x_1 \cdots x_n]$

Condition number growth with "column add" operation

Computational cost of finding only the eigenvalues

convergence of unshifted $QR$ algorithm proof

What do these matrices converge to?

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