Determinant Definition and 494 Threads

Hello all :) Homework Statement I'm trying to understand the fundamentals of General Relativity, but alas, I seem to be unable to grasp the fundamentals of variational calculus. Specifically, I'd like to prove the following relation for the square root of the negated determinant of the...

[FONT="Arial Black"][SIZE="7"]SOLVED 1. show that the determinant of a unitary matrix is a complex number of unit modulus 2. i know the equation for a determinant, but i guess to i am not sure what a complex number of unit modulus is either. I'm looking for...

Hi, can anyone give me an hint to proof the relation det(I + x A) = 1 + x tr A + O(x^2) thank you.

Homework Statement I have the matrix A as being (-2 3 2; 6 0 3; 4 1 -1) and I'd like to calculate its determinant via calculating its cofactor matrix, even if I know it's much more laborious than just calculating its determinant. I've calculated its cofactor matrix as being (-3 18 6; 5 -6...

-1. Homework Statement Let A and B be 2x2 matrices such that A²B=3I and A^T*B³=-I, where A^T is the transposed matrix of A, and I is the identity matrix. Calculate det(A). 0. The attempt at a solution I know I don't know how to approach correctly the problem, but I've tried something. I...

i am given 2 matrices A= a1 b1 c1 a2 b2 c1 a3 b3 c3 B= -c2 3c1 -c3 b2 -3b1 b3 -5a2 15a1 -5a3 and also given is: 5detA+detB=10 what i need to fin is det(3A2B-1) what i did to help me was det(3)=27...

Determine whether the given map \varphi is an isomorphism of the first binary structure with the second. < M2(R ), usual multiplication > with <R, usual multiplication> where \varphi(A) is the determinant of matrix A. The determinant of the matrix is ad-bc, so \varphi(A)=ad-bc. For this...

Hi, every one I'm newbie here. I have a few problem with my study about GR. Here's a problem \partial_a(g^{ad})g_{cd}-\partial_d(g^{ad})g_{ac}=\\0 Could I prove these relation by change index (in 1st term ) from a -> d and also d -> a? and let's defined {g}=det{\\g_{ab}\\}...

Homework Statement Let A be a 3 x 3 matrix. Consider the function f(A) = a11a22a33; g(A) = a11 a12 a13 and h(A) =1. Show that each of these is not a determinant function. Homework Equations det(I) = 1 det(B) = det(A) (if B is obtained from adding a mutiple of one row of A to another...

Not a problem par se, as much as me failing somewhere in algebra, and i can't find my mistakes. Trying to work through the secular determinant E_\pm = det\left( \begin{array}{cc} \alpha - E & \beta - ES\\ \beta - ES & \alpha - E \end{array}...

Hello! I am having problems with the inverse function theorem. In some books it says to be locally inversible: first C1, 2nd Jacobian determinant different from 0 And I saw some books say to be locally inversible, it suffices to change the 2NDto "F'(a) is bijective".. How could these two be...

Anyone having any ideas about how this formula could be proved? \underset{k<l}{\prod_{k,l=1}^n} (x_k - x_l) = (-1)^{n(n-1)/2} \left|\begin{array}{ccc} 1 & \cdots & 1 \\ x_1 & \cdots & x_n \\ \vdots & & \vdots \\ x_1^{n-1} & \cdots & x_n^{n-1} \\ \end{array}\right| I tried...

Homework Statement 1. Give an example of a 2x2 real matrix A such that A^2 = -I 2. Prove that there is no real 3x3 matrix A with A^2 = -I Homework Equations I think these equations would apply here? det(A^x) = (detA)^x det(kA) = (k^n)detA (A being an nxn matrix) det(I) = 1 The...

Homework Statement The determinant a+1 a a a b b+1 b b c c c+1 c d d d d+1 equals =? option : a) 1+ a + b+ c+ d b)a + b+ c+ d c)a.b.c.d d)1 + a.b.c.d Homework Equations The Attempt at a Solution [1] tried using finding...

Let there be a 2-by-2 matrix A with the elements: [a b] [c d] Now, let there be a 2-by-2 matrix B with the elements: [w x] [y z] Let A*A = B. This means that w, x, y, and z can all be independantly represented solely in terms of a, b, c, and d. My question: is there any way...

Determinant formula in monomials -- can it be generalized? I ran across this question in one of the Usenet groups (fr.sci.maths), and after doing a double take and realizing what was actually being asked I realized I don't know the answer, and after searching a bit I haven't turned it up, so I...

I don't understand this : let A is n x n matrix whose entries are precisely the numbers 1, 2, . . . , n^2. Put odd numbers into the diagonal of A, only even numbers above the diagonal and arrange the entries under the diagonal arbitrarily. Then det(A) is odd. What is the explanation ?

I understand that a chemical reaction is spontaneous if it has a (-) gibbs free energy = if it is endergonic. My question is: Why is energy the ultimate determinant of spontaneity

Everything I have read indicates that the cross product is simply defined as a x b = i( ay*bz - az*by) - j( ax*bz - az*bx ) + k( ax*by - ay*bx ) and that it just so happens that there is a shorthand notation of cross product in matrix determinant form. How is the cross product...

Homework Statement | x x^2 1 | | x^2 x 1 | | x^3 x^3 1 | The answer is = x^2(1-x)^2(1+2x) Homework Equations none The Attempt at a Solution By factoring the matrix step by step. Thanks :)

The question on my homework says: What can you say about the graph of the equation The following is in matrix form with determinant symbols around the matrix x y 1...

Need some help on how to prove this: Let A and B be two non-zero square matrices of n x n, if AB = 0n, then det(A) and det(B) must both equal to 0. I know if det(AB) = 0, then det(A) or det(B) must be 0, but here the question states that they must both be 0. Appreciate any help, thanks.

Ok, I have gotten different answers by reducing to an upper triangle, co-factor, and my calculator. All 3 giving me different answers! |Upper-triangle| = lol, was looking at the wrong problem ... I did get 36. |Co-factor reduction mobob| = uh i keep messing it up |Calculator| = 36 1 2 3 0 2 6...

I am trying to figure out the formula for the determinant of a 10x10 matrix. I was told to use row reducation method, but I am not really sure what it is. I never took Linear Algebra. Can someone please help me.

http://users.on.net/~rohanlal/11Untitled.jpg How do I find the value of a for which there will be no solution? Do you find the determinant, equate it to 0 and solve for a?

Homework Statement symmetric 2 × 2 matrices to V.Find the determinant of the linear transformation T(M)=[1,2,2,3]M+[1,2,2,3] from the space V of symmetric 2 × 2 matrices to V. Homework Equations The Attempt at a Solution hi this is my first post so if I break a rule please...

[SOLVED] linear algebra determinant of linear operator Homework Statement Let T be a linear operator on a finite-dimensional vector space V. Define the determinant of T as: det(T)=det([T][SIZE="1"]β) where β is any ordered basis for V. Prove that for any scalar λ and any ordered basis...

Can somebody help me in finding a determinat of a matrix of any dimension using C? This is in order to form an interpolating formula using the Newton Gregory Method.

Does it mean anything in particular about the transformation if the determinant of a transformation matrix is 1?

Homework Statement Find the eigenvalues and eigenvectors of A = \left(\begin{array}{ccc}5&1&1\\1&3&1\\1&1&3\end{array}\right) The Attempt at a Solution The problem I'm having is finding the eigenvalues for the matrix. In 2d matricies it's not too bad, but in 3d the...

Hi, After obtaining the 2D rotation matrix (as a function of rotation angle) once by geometry and once by complex algebra, I tried to obtain it by invariance of the Euclidean metric. By this approach, the four elements of the 2D rotation matrix can be determined in terms of a single...

Hi, I can't understand why any determinant expansion is the same via any row/column. My lecturer says the proof is too technical to go over, Does anyone have a good way to think about it intuitavely or know a site which has a full proof? thnx

If a 4X4 matrix A with rows v1, v2, v3, and v4 has determinant det A = -8 then det |(4v1+3v4)| |___v2___| |___v3___| =? |(8v1+9v4)| - I put the underscores for spacing.The Attempt at a Solution - I haven't attempting anything on this problem. There are no examples even remotely like this...

M= |3-2x^3_____-4+2x^2+4x^3______0| |-x^3________1+x^2+2x^3_______0| |-8-6x^2_____16+12x^2____-1-3x^2| find the determinant. * I put the underscores for spacing.The Attempt at a Solution I first tried finding det(A) as if it was a regular matrix of numbers, but that doesn't...

Homework Statement I have to proove that the determinant of : x a a . . . a a x a . . . a . . . . . . a . . . a a . . . . . x If you get the idea (it's (n x n) with x's along the diagonal and a's everywhere else) That it is (x + (n-1)a)(x - a)^(n-1)...

[SOLVED] 4x4 determinant using upper triangular form Homework Statement |2 0 1 4| |3 2 -4 -2| |2 3 -1 0| |11 8 -4 6| Homework Equations Ive done this a number of times and i still can't get the answer. I ended up w/ 275, but the answer is suppose to be zero The...

What does a determinant do exactly (what is it)? And what is the general method of calculating it?

[SOLVED] probability a determinant is odd Homework Statement The elements of a determinant are arbitrary integers. Determine the probability that the value of the determinant is odd. (Hint: Work mod 2).Homework Equations The Attempt at a Solution When n=1, the probability is 1/2. When n = 2...

Prove if A is orthogonal matrix, then |A|=+-1 A^{-1}=A^{T} AA^{-1}=AA^{T} I=AA^{T} |I|=|AA^{T}| 1=|A|*|A^{T}|//getting to the next step is where i get confused. Why is |A|=|A^{T}| 1=|A|*|A| 1=|A|^{2} +-1=|A|

I need help with proof. Can anyone lead me in the right direction? http://i153.photobucket.com/albums/s208/nailbomb2/LastScan.jpg

Hi I had a final today and one of the questions was find all the possible values of det Q if Q is a orthogonal matrix I m still wondering how would I do this? Any ideas?

[SOLVED] Determinant of Matrices Find the det. of the matrix: 1 3 -2 2 3 0 -1 4 1 -3 4 2 2 3 -3 3 Using gaussian elimination to get it into upper triangular form (which I think is easiest) is where I am struggling. I get as far as: 1 3 -2 2 0 -9 5 -2 0 -6 6 0...

Hi, I have a midterm tomorrow for my Lin Alg course and I was doing some review probs and I can't seem to understand this one.. http://img119.imageshack.us/img119/239/39786409wb4.jpg Can someone help me and explain how to do this one! I know I can just find the whole vector...

Q: Suppose A is a Hermitiain matrix, prove that det A is real. Note: I know nothing about inner products yet. Some thoughts: Perhaps proving that det A = conjugate of (det A) ? But how? Can someone please help me? Thanks!

Homework Statement A is a k by k matrix, B is a k by l matrix, D is an l by l matrix. Let M be the (k+l) by (k+l) matrix that has A in the upper left, B in the upper right, D in the lower right, and 0 in the lower left. Show that det(M) = det(A) det(D)Homework Equations The Attempt at a Solution

I just wanted to know that the following statement is always true or not. After I expand the determinant I get the value of the determinant as zero, ie. I know that the value of the determinant zero. Then with the help of row or column transformations can we transform the determinant into...

Homework Statement it is problem 1 on the attachment Homework Equations detA = ad - bc for a 2 x 2 matrix, where the first column is a c and the 2nd column is b d The Attempt at a Solution ah i see the first part i think, but I am nto sure I am writing my answer in the most...

[SOLVED] Determinant problem Homework Statement If det(A) = 7, then what is det(4 A-1)? where A is 3*3 matrix Homework Equations The Attempt at a Solution No idea about this, please give me some hint.

given the functional integral with 'g' small coupling constant \int \mathcal D [\phi]exp(iS_{0}[\phi]+\int d^{4}x \phi ^{k}) so k >2 then could we use a similar 'Functional determinant approach' to this Feynman integral ?? in the sense that the integral above will be equal to...

I say what is a functional determinant ?? for example Det( \partial ^{2} + m) is this some kind of Functional determinant? then i also believe (althouhg it diverges ) that Det( \partial ^{2} + m)= \lambda_{1}\lambda_{2}\lambda_{3}\lambda_{4}... (the determinant of a Matrix is the...