Determinant Definition and 494 Threads

Homework Statement Homework Equations The Attempt at a Solution

Has anyone seen this before? Is this true? $$ \begin{vmatrix} a & b+c & 1\\ b & a+c & 1\\ c & a+b & 1 \end{vmatrix} = \begin{vmatrix} a & b & 1\\ b & a & 1\\ c & a & 1 \end{vmatrix} + \begin{vmatrix} a & c & 1\\ b & c & 1\\ c & b & 1 \end{vmatrix} $$ In this example this works but I don't know...

Homework Statement Find the determinant of: |1 1| |2 1| The field is Z3. Homework Equations The field is Z3, that is, to multiply two numbers, you first multiply then take the remainder of the division by 3. The Attempt at a Solution I tried: ( 1 x 1 ) - ( 1 x 2 ) 1 x 1 will...

Homework Statement Solve for the wavefuntions using the Secular Determinant, of cyclopropene anion/cation/whocares. Homework Equations Secular determinant: | x 1 1| | 1 x 1| |1 1 x | The Attempt at a Solution I'm literally understanding every aspect of this concept, but...

Matrice $$c_n$$ is a 2nxn2 matrice and is given by $$(\delta_{ij}+2\delta_{i,2n-j+1})_{ij}$$ determine the expression of $$|c_n|$$ progress: I have been drawing the matrice $$n=1,2,3$$ and calculate the determinant. As you see there is a pattern with the matrice and I would like to have tips...

Homework Statement Hey guys, I usually have no trouble with 3x3 matrices, and for a 4x4 I've a rough idea how to do it but not entirely sure if I did it correct. I've attached my attempt below with working out. The matrix: \begin{pmatrix} 0 & 2 & 0 & 0 \\7 & a+1 & 3 & a+1 \\1 & 0 & 2 &...

Homework Statement Homework Equations The Attempt at a Solution I have already proved that ## N(T) \supset span\{y_{1},y_{2},...y_{n} \} ## but am having trouble proving the other half. You can't use the fact that the determinant is 0 to conclude that functions are linearly dependent unless...

Homework Statement Let F: x^2 + y^2 - z^2 + 2xy - 1 = 0 and G: x^3 + y^3 - 5y - 4 = 0. Calculate dz/dx. Note: This is NOT the partial derivative ∂z/∂x. I do not need help in taking the derivative of many polynomials. What I need help in is setting up a Jacobian determinant to evaluate this...

The Cauchy expansion says that \text{det} \begin{bmatrix} A & x \\[0.3em] y^T & a \end{bmatrix} = a \text{det}(A) - y^T \text{adj}(A) x , where A is an n-1 by n-1 matrix, y and x are vectors with n-1 elements, and a is a scalar. There is a proof in Matrix Analysis by Horn and...

If two matrices are similar, it can be proved that their determinants are equal. What about the converse? I don't think it is true, but could someone help me cook up a counterexample? How does one prove that two matrices are not similar? Thanks! BiP

Hello folks! Just a concise introduction of myself before I get to the task at hand: I'm new to these forums although I have been surfing them frequently for the past 5 years! I am not a math major and quite frankly, my skills in the subject are limited. Be that as it may, my fascination for...

Homework Statement A while ago someone posted this problem: ----------------------------------------------------------------------------------- Problem 1 (given after a discussion of determinants in week 3/4 of the course): Consider a 9x9 matrix A. We say that A is a Sudoku matrix if it's...

Hello MHB, calculate determinant of: $$ \left| {\begin{array}{cc} 2 & -2 & -3 & 8 \\ 1 & -1 & 2 & -1 \\ -3 & 4 & 1 & -1 \\ -2 & 6 & -4 & 19 \end{array} } \right|$$ so I multiplication -2 row 2 and add it to row 1, multiplication 3 to row 2 and add it to row 3, multiplicate 2 to row 2 and add...

hi there, In this wikipedia article https://en.wikipedia.org/wiki/Electromagnetic_tensor we have the following invariant : FαβFμη [SIZE="3"]εαβμη = 8 E*B However the determinant is the square of this quantity divided by 8, i.e. ( E*B )2 . Now from the definition of the determinant...

Homework Statement Find the determinant of the matrix given by: \begin{array}{ccc} 1 & 2 & 3 & ... & n \\ 2 & 2 & 3 & ... & n \\ 3 & 3 & 3 & ... & n \\ . & . & . & & . \\ . & . & . & & . \\ . & . & . & & . \\ n & n & n & ... & n \end{array} Homework Equations We...

How to use Slater determinant and permanent to find out whether the state is symmetrical or anti-symmetrical? How to use them? I got the concept but I didn't get for example when to know if there was a plus or a minus and thus whether what we're talking about is a permanent or determinant...

Homework Statement Evaluate the appropriate determinant to show that the Jacobian of the transformation from Cartesian (this is a typo, they mean spherical) pψθ-space to Cartesian xyz-space is ρ2sin(ψ).Homework Equations The Attempt at a Solution Uhm, I am lost. I'm supposed to prove that when...

I am curious on how the determinant function determines orientation? I read about in in one of Werner greubs books and I just cannot manage to understand what it is

it seems to have many different ways to express a determinant, when we are using indices to write vectors and tensors, e.g. in General Relativity. is there any summary about how to express a determinant, for example, in Levi-Civita Tensor and so on?

Is there a nice way to show that Det(AB)=Det(A)Det(B) where A and B are n x n matrices over a commutative ring? I'm hoping there is some analogue to the construction for vector spaces that defines the determinant in a natural way using alternating multilinear mappings... Otherwise would...

Let $F$ be any field. Let $p_1,\ldots, p_n\in F[x]$. Assume that $\gcd(p_1,\ldots,p_n)=1$. Show that there is an $n\times n$ matrix over $F[x]$ of determinant $1$ whose first row is $p_1,\ldots,p_n$. When $n=2$ this is easy since then there exist $a_1,a_2\in F[x]$ such that $p_1a_1+p_2a_2=1$...

Homework Statement Lets find the determinant of 1 1 1 1 ... 1 1 2 2 2 ... 2 1 2 3 3 ... 3 1 2 3 4 ... 4 ... 1 2 3 4 ... n The Attempt at a Solution In class, we solved it by subtracting the previous line of every single line, ending up with 1 1 1 1 ... 1 1 2 2 2 ... 2...

How to calculate something relating to the determinant of metric tensor? for example, its derivative ∂_{λ}g. and how to calculate1/g* ∂_{λ}g, which is from (3.33) in the book Spacetime and Geometry, in which the author says that it can be related to the Christoffel connection.

Homework Statement I am looking for the base, collector, and emitter voltages in the following circuit: Homework Equations KCL KVL offset voltage = VB - VE saturation voltage = VC - VE The Attempt at a Solution First I made a matrix without assuming any values for offset or...

Do you know where can I find proven identity det(AB)=det(A)det(B) using Levi Civita symbol.

Hi can anyone explain how to find \delta \sqrt{-g} when varying with respect to the metric tensor g^{\mu\nu}. i.e why is it equal to \delta \sqrt{-g} = -\frac{1}{2} \sqrt{-g}g_{\mu\nu} \delta g^{\mu \nu}

Homework Statement Let A and B be nxn matrices. Prove that if AB=I, then BA=I det(AB)=det(I) 1.det(A)*det(B)=1 det(BA)=det(I) 2.det(B)*det(A)=1 Equating 1 and two together I get det(B)*det(A)=det(A)*det(B) Thus AB=I, then BA=I Is this correct? Homework Equations...

Homework Statement Given A=[1 2 1; 0 4 3; 1 2 2] determine the (2,3) entry of A-1 by computing a quotient of two determinants. This problem confused me a bit, do they just want us to divide the adj(A) by the det(A) in order which would give us A-1 and just state the (2,3) entry from...

Hi does anyone know how to calculate: \delta (det|g_{\mu\nu}|) or simply \delta g

We are stating with equivalence principle that passing locally to non inertial frame would be analogous to the presence of gravitational field at that point, so g^'_{ij}=A g_{nm} A^{-1} where g' is the galilean metric and g is the metric in curved space, and A is the transformation which...

I'm looking for the deeper meaning behind this law/theorem/statement (I don't know what it is, please correct me). My textbook just told us a matrix is not invertible if the determinant is zero.

In what kind of math course would one learn the proof of the theorem that introduces the Jacobian to computing multiple integrals under various transformations? My calculus textbook has this theorem, and uses it to derive the triple integral formulas for cylindrical and spherical coordinates...

Hi All, I'm trying to solve the following derivative with respect to the scalar parameter \sigma $$\frac{\partial}{\partial \sigma} \ln|\Sigma|,$$ where \Sigma = (\sigma^2 \Lambda_K) and \Lambda_K is the following symmetric tridiagonal K \times K matrix $$ \Lambda_{K} = \left(...

Hello! Do somebody know where the code for calculating a determinant by Laplace theorem (in Fortran) can be found? Or maybe somebody could help with this issue. Thank you!

Hi, I'm tutoring someone on lineal algebra (upper high-school level). We're going through some exercises, but we're stuck with a trivial looking one. Homework Statement Show that the following determinant is null: \left| \begin{array}{ccc} 1 & \cos x & \cos 2x \\ \cos x & \cos 2x &...

Homework Statement I have this 4x4 determinant and usually these are just mechanical work, until I stumbled upon one containing x, how should one go about solving these type of determinants? [x 2x 4 x ] [1 2 2x 1 ] [2x x-1 2 3x] [ 2 x+1 x+3 x-1] What are the different values of...

Hi. Here is a problem I found in my algebra book and I don't know how to solve it. Could you please help me? Show that there exists a matrix A \in M(n,n;R), such that m_{ij} \in \{-1,0,1\} and det A=1995 (I think it can be any other number as well, but the book was printed in 1995 :) ) My...

Hello everyone, I found that you're actively discussing math problems here and thought to share my problem with you. [Givens:] I have a specially structured complex-valued n \times n matrix, that has only three non-zero constant diagonals (the main diagonal, the j^{th} subdiagonal and the...

am not a math guru :P,am a newbie even if this should be solved by a newbie as well, Id like u guys to help me out to solve this one : 3x-y+2z=4 Im really needing this, thank you all.

Hello Could anyone give an intuitive explanation of the determinant? I know mostly what the determinant means and I can calculate it etc. But I have never got any real-world intuitive explanation of the general formula of the determinant? How is the formula derived? Where does it come...

Hi, Homework Statement I was asked to find the determinant of the following two matrices (please see attachment). Homework Equations The Attempt at a Solution I know that the determinant of the matrix on the left is [(-1)^(n-1)]*(n-1), but I have no idea how to formally derive...

Determinant of "enlarged" Correlation Matrix Hi guys, I am not a physicist but saw that you guys are actively discussing math problems in this forum. I have the following problem that I've been fighting with for some time now: I have a n-dimensional (n >= 3) correlation matrix with the...

Not sure if this is where I should put this but currently I am taking math for econ and we are on special determinants (jacobian, Hessian, Bordered Hessian, some Leontiff) So I have this problem in my notes that I am basically basing my exam studying around since the book isn't the best. It...

Homework Statement This is not homework but more like self-study - thought I'd post it here anyway. I'm taking the variation of the determinant of the metric tensor: \delta(det[g\mu\nu]). Homework Equations The answer is \delta(det[g\mu\nu]) =det[g\mu\nu] g\mu\nu...

Homework Statement Mesh Analysis, find current z: A= \left(\begin{array}{ccc}+30x&-15y&-15z\\-15x&+30y&-15z\\-15x&-15y&+30z\end{array}\right) b= \left(\begin{array}{c}+10\\-10\\0\end{array}\right) Homework Equations A*x=b A= resistance x= currents b= voltage sources Gauss elimination...

Hello, it is true that linear transformations have constant Jacobian determinant. Is the converse true? That is, if a transformation has constant Jacobian determinant, then is it necessarily linear?

I am curious about the proof of the fact that the value of a determinant computed using the Laplace (or cofactor) expansion is independent of along which row (or column) the expansion is performed. Is this a very difficult proof? My textbook omits it entirely. I was curious if someone could...

I am reading the paper http://arxiv.org/abs/hep-th/9701037. In equation (2), the author write the determinat as traces, but I don't know how to do this. I know that ##det(e^A)=e^{tr(A)}##, where ##A## is a complex matrix, and ##det(A)=e^{tr(L)}##, where ##e^L=A## and ##L## is also a complex...

Homework Statement As you can see from the picture below this a 4x4 matrix with an unknown value, λ. My objective here is to find four values for λ so that the determinant of the 4x4 matrix is equal to zero. http://i49.tinypic.com/n4cenn.png Homework Equations The above 4x4 matrix is the...

Homework Statement The problem is attached due to it not being able to copy over the given matrix.. Number 5.3 Homework Equations The Attempt at a Solution I tried to compute A+tI and then row reduce until A+tI was a triangle matrix and then multiply the diagnol entries but I got...