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Algebra

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A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Multiplication chart! :)

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2x1

2x2

2x3

2x4

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Math and Arithmetic

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The length of a rectangular floor is 2 feet more than its width The area of the floor is 168 square feet Kim wants to use a rug in the middle of the room and leave a 2 foot border of the floor visib

The perimeter of a rectangle is 18 feet and the area of the rectangle is 20 square feet what is the width of the rectangle

The sum of two numbers is 19 and their product is 78 What is the larger number

A rectangular garden has a perimeter of 48 cm and an area of 140 sq cm What is the width of this garden

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Q: What is significance of eigenvectors of a matrix?
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Related questions

Can a Hermitian Matrix possess Complex Eigenvectors?

Yes. Simple example: a=(1 i) (-i 1) The eigenvalues of the Hermitean matrix a are 0 and 2 and the corresponding eigenvectors are (i -1) and (i 1). A Hermitean matrix always has real eigenvalues, but it can have complex eigenvectors.


What is Eigen analysis?

Eigenvalues and eigenvectors are properties of a mathematical matrix.See related Wikipedia link for more details on what they are and some examples of how to use them for analysis.


Do similar matrices have the same eigenvectors?

No, in general they do not. They have the same eigenvalues but not the same eigenvectors.


What are eigenvalues and eigenvectors?

An eigenvector is a vector which, when transformed by a given matrix, is merely multiplied by a scalar constant; its direction isn't changed. An eigenvalue, in this context, is the factor by which the eigenvector is multiplied when transformed.


What is the eigen value?

This is the definition of eigenvectors and eigenvalues according to Wikipedia:Specifically, a non-zero column vector v is a (right) eigenvector of a matrix A if (and only if) there exists a number λ such that Av = λv. The number λ is called the eigenvalue corresponding to that vector. The set of all eigenvectors of a matrix, each paired with its corresponding eigenvalue, is called the eigensystemof that matrix


What are eigen values and eigen vectors?

This is a complicated subject, which can't be explained in a few words. Read the Wikipedia article on "eigenvalue"; or better yet, read a book on linear algebra. Briefly, and quoting from the Wikipedia, "The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain parallel to the original vector. For each eigenvector, the corresponding eigenvalue is the factor by which the eigenvector is scaled when multiplied by the matrix."


Is eigenvalue applicable only to n x n matrices?

The answer is yes, and here's why: Remember that for the eigenvalues (k) and eigenvectors (v) of a matrix (M) the following holds: M.v = k*v, where "." denotes matrix multiplication. This operation is only defined if the number of columns in the first matrix is equal to the number of rows in the second, and the resulting matrix/vector will have as many rows as the first matrix, and as many columns as the second matrix. For example, if you have a 3 x 2 matrix and multiply with a 2 x 4 matrix, the result will be a 3 x 4 matrix. Applying this to the eigenvalue problem, where the second matrix is a vector, we see that if the matrix M is m x n and the vector is n x 1, the result will be an m x 1 vector. Clearly, this can never be a scalar multiple of the original vector.


Do commutative matrices have the same eigenvectors?

It is true that diagonalizable matrices A and B commute if and only if they are simultaneously diagonalizable. This result can be found in standard texts (e.g. Horn and Johnson, Matrix Analysis, 1999, Theorem 1.3.12.) One direction of the if and only if proof is straightforward, but the other direction is more technical: If A and B are diagonalizable matrices of the same order, and have the same eigenvectors, then, without loss of generality, we can write their diagonalizations as A = VDV-1 and B = VLV-1, where V is the matrix composed of the basis eigenvectors of A and B, and D and L are diagonal matrices with the corresponding eigenvalues of A and B as their diagonal elements. Since diagonal matrices commute, DL = LD. So, AB = VDV-1VLV-1 = VDLV-1 = VLDV-1 = VLV-1VDV-1 = BA. The reverse is harder to prove, but one online proof is given below as a related link. The proof in Horn and Johnson is clear and concise. Consider the particular case that B is the identity, I. If A = VDV-1 is a diagonalization of A, then I = VIV-1 is a diagonalization of I; i.e., A and I have the same eigenvectors.


What are all the matrix movies?

Matrix, Matrix Reloaded, Matrix Revolution Matrix, Matrix Reloaded, Matrix Revolution.


Does the name Neo have any significance in the movie The Matrix?

Yes. Neo is an anagram of One, a reference to his destiny of being The One who would bring peace.


What type of matrix is a vector?

Vector matrix has both size and direction. There are different types of matrix namely the scalar matrix, the symmetric matrix, the square matrix and the column matrix.


What was first matrix revolution or matrix reloaded?

The first movie was "The Matrix", the second was "Matrix Reloaded", then "Matrix Revolutions".


What is a reduced matrix?

Reduced matrix is a matrix where the elements of the matrix is reduced by eliminating the elements in the row which its aim is to make an identity matrix.


Is matrix polynomial and polynomial matrix same?

No. A matrix polynomial is an algebraic expression in which the variable is a matrix. A polynomial matrix is a matrix in which each element is a polynomial.


What are the The Matrix?

There are three Matrix movies: The Matrix, The Matrix Reloaded, and The Matrix Revolutions. There are also a series of short animated films called The Animatrix.


Is there any matrix called as zero matrix?

ya yes its there a matrix called zero matrix


What is the order of The Matrix?

The Matrix The Matrix Reloaded The Matrix Revolutions


How do you call a matrix that if you multiplied it by the original matrix you would get the identity matrix?

That is called an inverse matrix


What is idempotent matrix?

An idempotent matrix is a matrix which gives the same matrix if we multiply with the same. in simple words,square of the matrix is equal to the same matrix. if M is our matrix,then MM=M. then M is a idempotent matrix.


When was the Matrix the movie made?

The Matrix: 1999 The Matrix Reloaded: 2003* The Matrix Revolutions: 2003* *The Matrix Reloaded and Revolutions were made at the same time as so was Enter The Matrix video game.


What are the matrix movies?

There are three Matrix movies: The Matrix, The Matrix Reloaded, and The Matrix Revolutions. There are also a series of short animated films called The Animatrix.


How are the inverse matrix and identity matrix related?

If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.


What is the order of the matrix films?

The Matrix The Matrix Reloaded The Matrix Revolutions


What is the order of the Matrix Series?

The Matrix The Matrix Reloaded The Matrix Revolution


What are the names of the 3 Matrix movies?

The first Matrix movie is called 'The Matrix' and is from 1999. The second one is called 'The Matrix Reloaded' and is from 2003. Also the third Matrix movie is from 2003: 'The Matrix Revolutions'.