Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [numerical-linear-algebra]

Questions on the various algorithms used in linear algebra computations (matrix computations).

Questions tagged with this tag can be about, but not limited to:

  1. Matrix decompositions like SVD, QR, Cholesky, etc.
  2. The solution of linear systems and least squares problems.
  3. Analysis of numerical linear algebra algorithms like condition numbers and stability analysis.
  4. Eigenvalue problems.
  5. The designs of direct or iterative methods to solve linear systems.
3541 questions
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vector space of natural numbers

I wonder, is it possible for the natural numbers (with zero) t be a vector space on SOME field? I understand why it cannot be over real numbers because of muliplication with negative scalar. BUT what about modulo3 field that have only positive…
sharonb
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1 answer

Solving Linear Least Squares for polynomial fitting, ill-conditioned

In trying to fit polynomials to data, I have a tall and skinny matrix $A$, of size $\simeq 250,000 \times 1000$, that is quite ill-conditioned $\kappa(A) \simeq 10^{78}$. I am solving it by pivoted QR, but the results get worse when adding more…
user288227
  • 308
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2 answers

Profit and Loss, Finding Selling price

An article was sold at 10% profit. Had it been purchased at Rs 22 more and sold at 5% more, the profit remains same. Find the SP to gain a profit of 62.5%?
thespoiledboy
  • 9
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1 answer

Multiplicity of eigenvalues of preconditioned matrix

I have a symmetric positive definite (SPD) matrix $A\in\mathbb{R}^{n\times n}$ and a full-rank matrix $B\in\mathbb{R}^{m\times n}$. I know that the pre-conditioned matrix $\begin{bmatrix} A & 0 \\ 0 &…
HBHSU
  • 699
-1
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1 answer

Solving a matrix least squares problem with a fixed Frobenius norm constraint

I am trying to solve for X an equation of the form : Min ||AXB-CXD|| s.t. ||X||_F=1, where , A, C are m-by-m matrices, and B, D are n-by-b matrices. Is there any effective algorithms? Any hint is greatly appreciated :-)
Jiao-fen Li
  • 1
-2
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2 answers

Following number is divisible by

If $ n = 2009$ , then $N = 2009^n -1982^n -1972^n + 1945^n $ is not divisible by 659 1977 1998 2009
Aakash Kumar
  • 3,480
-3
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A mathematic problem

Our teacher gave us a question but she didn't explain it. How to solve it? $x^2+ \frac{1 }{x^2}=27$ Find, $x+ \frac{1}{x}$ and $x- \frac{1}{x}$ I am new to maths jax so sorry.
Rajdeep Singh
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