Questions tagged [linear-algebra]
For questions on linear algebra, including vector spaces, linear transformations, systems of linear equations, spanning sets, bases, dimensions and vector subspaces.
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Possible number of Jordan canonical forms
Let $A = [a_{ij}]_{n \times n}$ and suppose the minimal polynomial is
$ m_A(x) = (x-2)^4 (x-1)^4 $
How many Jordan canonical forms are possible?
Since the exponent 4ドル$ forces the largest Jordan block ...
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If 2 recursion relation has the same coeficients are the solution proportional?
In the book of sakurai
Modern Quantum Mechanics they have this $$
\begin{aligned}
& \sqrt{(j \mp m)(j \pm m+1)}\left\langle j_1 j_2 ; m_1 m_2 \mid j_1 j_2 ; j, m \pm 1\right\rangle \\
& =\sqrt{...
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What is the Big Picture of Linear Algebra? [closed]
I am currently learning about linear algebra. To better understand linear algebra and create a network of mathematical concepts, I would like to know what the Big Picture of Linear Algebra is. Which ...
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can a pivotal variable be equal to zero using gauss elimination method, even if you have your AX= B where b is defined to be 1/2 [closed]
Find the solution of the following linear system using the Gauss elimination method:
x1 + 2x2 − x3 + x4 = 3,
2x1 − x2 + x3 + x5 = 2,
3x1 + x2 + x4 − x5 = 4
The particular solution is same as chatgpt ...
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Quotient group technicality
I'm studying linear Algebra by myself right now and I'm currently reading about quotient groups. I wanted to disprove the following: for two normal subgroups $N_1\subseteq N_2$ of $(G,\cdot),ドル $G/N_2$ ...
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Most general Logarithm of a matrix
Consider any matrix $A \in \text{GL}_d(\mathbb{C}),ドル i.e, a square invertible matrix. We define a logarithm of $A$ as any matrix $X$ such that $$e^X = A.$$
Our objective is to find of possible ...
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Solving for a diffraction grating's orientation and surface periodicity from its diffracted beams, can the problem be inverted?
Background:
Below is a calculation of the diffracted wavevector $\mathbf{k_1}$ from an initial wavevector $\mathbf{k_0} = -k_0 \mathbf{\hat{z}}$ incident on a planar surface with normal $\mathbf{\hat{...
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Showing the Cayley transform sends positive definite matrices to small matrices and vice versa
Given a matrix $Z\in\Bbb R^{n\times n},ドル write $Z\succ0$ to mean that $\langle v,Zv\rangle>0$ when $v\ne0$. (We may say that $Z$ is positive definite, but note that $Z$ is not required to be ...