Matrix Definition and 999 Threads

Say, I have a matrix which I obtained from a website for matrix calculation, how to insert it into an excel so as for each cell in the matrix, there is a corresponding cell in the excel sheet?

Homework Statement How to calculate the matrix elements of the quantum harmonic oscillator Hamiltonian with perturbation to potential of -2cos(\pi x) The attempt at a solution H=H_o +H' so H=\frac{p^2}{2m}+\frac{1}{2} m \omega x^2-2cos(\pi x) I know how to find the matrix of the normal...

Hello! I need to find the rotation matrix around a given vector v=(a,b,c), by and angle ##\theta##. I can find an orthonormal basis of the plane perpendicular to v but how can I compute the matrix from this? I think I can do it by brute force, rewriting the orthonormal basis rotated by...

Homework Statement For what ##h## is the matrix ##\begin{bmatrix}1 & -h^2 & 2h \\ 0 & 2h & h \\ 0 & 0 & h^2 \end{bmatrix}## diagonalizable with real eigenvalues? (More than one may be correct) a) -2, b) -1, c) 0, d) 1, e) 2 Homework EquationsThe Attempt at a Solution We already know the...

I would love to get help on this problem: Suppose that $M$ is a square $k \times k$ matrix with entries of 1's in the main diagonal and entries of $\frac{1}{k}$ for all others. Show that the rank of $M$ is $k$. I think I should go about by contradiction, that is, by assuming that the column...

Homework Statement If a 3 x 3 matrix A is diagonalizable with eigenvalues -1, and +1, then it is an orthogonal matrix. Homework EquationsThe Attempt at a Solution I feel like this question is false, since the true statement is that if a matrix A is orthogonal, then it has a determinant of +1...

Just a couple of quick questions on index notation, may be because of the way I'm thinking as matrix representation: 1) ##V^{u}B_{kl}=B_{kl}V^{u}## , i.e. you are free to switch the order of objects, I had no idea you could do this, and don't really understand for two reasons...

Homework Statement Suppose that a square matrix ##A## satisfies ##(A - I)^2 = 0##. Find an explicit formula for ##A^{-1}## in terms of ##A## Homework EquationsThe Attempt at a Solution From manipulation we find that ##A^2 - 2A + I = 0## and then ##A(2I - A) = I##. This shows that if we...

Let A be a 4×3 matrix and let c=2a1+a2+a3 (a) If N(A) = {0}, what can you conclude about the solutions to the linear system Ax=c? (b) If N(A) ≠ {0}, how many solutions will the system Ax=c have? Explain.

This might be a dumb question, but I am wondering, given the equation ##A\vec{x} - 7\vec{x} = \vec{0}##, the factorization ##(A - 7I)\vec{x} = \vec{0}## is correct rather than the factorization ##(A - 7)\vec{x} = \vec{0}##. It seems that I can discribute just fine to get the equation we had...

Let the matrix of partial derivatives ##\displaystyle{\frac{\partial y^{j}}{\partial y^{i}}}## be a ##p \times p## matrix, but let the rank of this matrix be less than ##p##. Does this mean that some given element of this matrix, say ##\displaystyle{\frac{\partial y^{1}}{\partial u^{2}}}##, can...

Homework Statement The system is a spring with constant 3k hanging from a ceiling with a mass m attached to it, then attached to that mass another spring with constant 2k and another mass m attached to that. So spring -> mass -> spring ->mass. Find the normal modes and characteristic system...

Hello, I was refreshing my Mathematics using S.M. Blinder's book "Guide to Essential Math" and on the section on Matrix Multiplication I got the following, Can someone elaborate on the highlighted section? In particular, what does "adjacent indices" mean? Thank you.

<< Mentor Note -- thread moved from Homework Help forums to General Math >>[/color] Good day, I run coding in Mathematica. But, I get singular matrix A at certain loop. In theory, how can I make matrix A become orthogonal A=\begin{pmatrix} 0& 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0& 0 & 0 & 0 & 0 &...

To me it seems basic question or even obvious but as I am not mathematician I would rather like to check. Is it true that these two matrices are both identity matrices: ##\begin{pmatrix}1&0\\0&1\end{pmatrix} ## and...

i don't understand how to get second box using first box in the picthure that has attached.could someone help me?

Hi. When referring to matrices what does ℝm x n mean ? Does this notation also apply to vectors ? Thanks

Extracted from 'At the frontiers of Physics, a handbook of QCD, volume 2', '...in the physical Bjorken ##x##-space formulation, an equivalent definition of PDFs can be given in terms of matrix elements of bi-local operators on the lightcone. The distribution of quark 'a' in a parent 'X'...

Hi, I know the generalized hookes law between stress and strain is given by the elastic tensor. This matrix has 81 constants which are reduced to 9 in the isotropic case. Can someone please help me to understand intuitively how this reduction in the elastic tensor takes place and why some of the...

I am working on this problem which has been baffling me since the beginning: Prove that $A^k = 0$ and $A^{k-1} \neq 0$ if $A_{k \times k}$ is a zero matrix but with entries of 1's right above its diagonal. For example, if $k = 3$ the it will look like this $$\begin{pmatrix} 0 &1 &0\\ 0 &0 &1\\...

Homework Statement Prove that the upper triangular matrices form a subspace of ##\mathbb{M}_{m \times n}## over a field ##\mathbb{F}## Homework EquationsThe Attempt at a Solution We can prove this entrywise. 1) Obviously the zero matrix is an upper triangular matrix, because it satisfies the...

I am confused about a transition matrix as I need to prove that if matrix A is positive, then A^(m+1) is also positive. However, when calculating the (m+1)th transition, I need to put matrix A on the left side of equation (A^m)x=x to write A(A^m)x=x. This to me represents after m times...

this is not a homework question, I just want to make sense of the equation here. Assuming matrix A is diagonal, If A_hat=T'AT where T' is an inverse matrix of T. e^(A_hat*t)=T'e^(At)T which implies, e^(T'AT*t)=T'e^(At)T we know that e^(At) is a linear mapping, therefore if we convert f to...

I am reading Louis Rowen's book, "Ring Theory"(Student Edition) ... I have a problem interpreting Rowen's notation in Section 1.1 Matrix Rings and Idempotents ... The relevant section of Rowen's text reads as follows: In the above text from Rowen, we read the following: " ... ... We obtain a...

I am reading Louis Rowen's book, "Ring Theory" (Student Edition) ... I have a problem interpreting Rowen's notation in Section 1.1 Matrix Rings and Idempotents ... The relevant section of Rowen's text reads as follows: In the above text from Rowen, we read the following: " ... ... We obtain...

Homework Statement I have to find the matrix system of Sx, Sy , and Sz using the given information: 190899[/ATTACH]'] Homework EquationsThe Attempt at a Solution for attempting Sx: Ignoring the ket at the bottom, I would get Sx|+> = +ħ/2[[0,1],[1,0]] but my question here is, does the ket at...

I am working on a two-by-two real matrix $M$, with a linear mapping $F$ that returns the sum of $M$ and its transpose. I need to find out the matrix that is associated with the mapping. To the best of my understanding: $$ M + M^T = \begin{bmatrix} r &s\\ t &u \end{bmatrix} + \begin{bmatrix} r...

Given a n x n matrix whose (i,j)-th entry is i or j, whichever smaller, eg. [1, 1, 1, 1] [1, 2, 2, 2] [1, 2, 3, 3] [1, 2, 3, 4] The determinant of any such matrix is 1. How do I prove this? Tried induction but the assumption would only help me to compute the term for Ann mirror.

This sounds like a common application, but I didn't find a discussion of it. Simple case: I have 30 experimental values, and I have the full covariance matrix for the measurements (they are correlated). I am now interested in the sum of the first 5 measured values, the sum of the following 5...

Homework Statement We're given some linear transformations, and asked what the null space, column space and row space of the matrix representations tell us Homework EquationsThe Attempt at a Solution I know what information the column space and null space contain, but what does the row space of...

Suppose that I have an overdetermined equation system in matrix form: Ax = b Where x and b are column vectors, and A has the same number of rows as b, and x has less rows than both. The least-squares method could be used here to obtain the best possible approximative solution. Let's call this...

We know that Poincare matrix which is 0 Kx Ky Kz ( -Kx 0 Jz -Jy ) describes the boost and rotation is very similar to -Ky -Jz 0 Jx...

Homework Statement (I'm trying to replicate some results in an academic paper where they have calculated elastic properties of a crystal. Because I'm going to do a lot of similar time-consuming calculations following this one, I need to learn how to do them using a computer.) The compliance...

I am reading T. Y. Lam's book, "A First Course in Noncommutative Rings" (Second Edition) and am currently focussed on Section 1:Basic Terminology and Examples ... I need help with Part (1) of Proposition 1.17 ... ... Proposition 1.17 (together with related material from Example 1.14 reads...

I am reading T. Y. Lam's book, "A First Course in Noncommutative Rings" (Second Edition) and am currently focussed on Section 1:Basic Terminology and Examples ... I need help with Part (1) of Proposition 1.17 ... ... Proposition 1.17 (together with related material from Example 1.14 reads as...

I am reading T. Y. Lam's book, "A First Course in Noncommutative Rings" (Second Edition) and am currently focussed on Section 1:Basic Terminology and Examples ... I need help with yet another aspect of Example 1.14 ... ... Example 1.14 reads as follows: Near the end of the above text from...

I am reading T. Y. Lam's book, "A First Course in Noncommutative Rings" (Second Edition) and am currently focussed on Section 1:Basic Terminology and Examples ... I need help with yet another aspect of Example 1.14 ... ... Example 1.14 reads as follows: Near the end of the above text from T...

Lets say I have a matrix A=rand(31,51). How can I extract its elements from its center (say row = 15, column = 26) in circular manner. I want to have a matrix that displays only those elements of 'A' which are inside a circle with its center at A(15,26). Radius of circle can be any number say 5...

The problem I have is this: Show that \begin{bmatrix} 1 & 1 & 1 \\ λ_{1} & λ_{2} & λ_{3} \\ λ_{1}^{2} & λ_{2}^{2} & λ_{3}^{2} \end{bmatrix} Has determinant $$ (λ_{3} - λ_{2}) (λ_{3} - λ_{1}) (λ_{2} - λ_{1}) $$ And generalize to the NxN case (proof not needed)Obviously solving the 3x3 was...

Homework Statement Show that the determinant of is (a-b)(b-c)(c-a) Homework Equations Row reduction, determinants The Attempt at a Solution Apparently I got a (a-b)^2 instead of (a-b) when I multiplied them up. It would be grateful if someone can point me out where the mistakes are.

I am new to linear algebra but I have been trying to figure out this question. Everybody seems to take for granted that for matrix A which has eigenvectors x, A2 also has the same eigenvectors? I know that people are just operating on the equation Ax=λx, saying that A2x=A(Ax)=A(λx) and...

I am very confused about that in some literature the Maurer Cartan forms for a matrix group is written as ##{\omega _g} = {g^{ - 1}}dg## what is ##dg## here? can anyone give an example explicitly? My best guess is ## dg = \left( {\begin{array}{*{20}{c}} {d{x^{11}}}& \ldots &{d{x^{1m}}}\\...

Homework Statement Let ##A## be an n × p matrix and ##B## be an p × m matrix with the following column vector representation, B = \begin{bmatrix} b_1 , & b_2, & ... & ,b_m \end{bmatrix} Prove that AB = \begin{bmatrix} Ab_1 , & Ab_2, & ... & , Ab_m \end{bmatrix} If ##A## is represented...

Suppose, ##A## is an idempotent matrix, i.e, ##A^2=A##. For idempotent matrix, the eigenvalues are ##1## and ##0##. Here, the eigenspace corresponding to eigenvalue ##1## is the column space, and the eigenspace corresponding to eigenvalue ##0## is the null space. But eigenspaces for distinct...

Hello, I was just wondering if there is a geometric interpretation of the trace in the same way that the determinant is the volume of the vectors that make up a parallelepiped. Thanks!

Homework Statement I have the matrix form of the Hamiltonian: H = ( 1 2-i 2+i 3) If in the t=0, system is in the state a = (1 0)T, what is Ψ(x,t)? Homework Equations Eigenvalue equation The Attempt at a Solution So, I have diagonalized given matrix and got...

Homework Statement Eigenvalues of the Hamiltonian with corresponding energies are: Iv1>=(I1>+I2>+I3>)/31/2 E1=α + 2β Iv2>=(I1>-I3>) /21/2 E2=α-β Iv3>= (2I2> - I1> I3>)/61/2 E3=α-β Write the matrix of the Hamiltonian in the basis of...

Homework Statement Show that the matrix ##P = \big{[} p_{ij} \big{]}## is orthogonal. Homework Equations ##P \vec{v} = \vec{v}'## where each vector is in ##\mathbb{R}^3## and ##P## is a ##3 \times 3## matrix. SO I guess ##P## is a transformation matrix taking ##\vec{v}## to ##\vec{v}'##. I...

Homework Statement Vectors I1> and I2> create the orthonormal basis. Operator O is: O=a(I1><1I-I2><2I+iI1><2I-iI2><1I), where a is a real number. Find the matrix representation of the operator in the basis I1>,I2>. Find eigenvalues and eigenvectors of the operator. Check if the eigenvectors are...

Homework Statement [/B] \begin{array}{cc}1 & 1&1\\ 1&1-s&1-s\\-s&1-s&s^2-1\end{array} a)For which values of s does the inverse exist, and why? You should be using row operations and ideally head for reduced row echelon form b) In the process of calculating part a), you will come across a...