What is orthogonal and normal matrix? Can every orthogonal matrix be normal matrix and vice versa.

Q: Can a matrix be similar to two different diagonal matrices? Explain.

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Q: Define Identity matrix ?

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Q: FIND THE FUNDAMENTAL MATRIX AS WELL AS THE FUND AMENTAR MATRIX ø (6)= I %3D SATISEYING x' = 2 -5 -2

A: Fundamental matrix is formed with linearly independent solution sets of the system. These linearly…

Q: I want to know about change of basis matrix and what does it mean by diagonalization of a matrix.

A: Change of Basis:

Q: Define bidiagonal matrix.

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Q: Determine if the matrix is diagonalizable

A: Given matrix, A=200-121101 we know that, if a matrix A is an n×n matrix, then it must have n…

Q: elementary

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Q: What is Orthoganal Matrix?

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Q: Define Hessian Matrix ?

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Q: Which one of the matrices below is singular( Not invertible )?

A: A matrix whose determinant is zero is called as a singular matrix. Let us verify the options. (a)…

Q: Show that the product of two orthogonal matrices is also an orthogonal matrix. Is the product of two…

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Q: What is mean by Matrix? Define elements matrix?

A: Matrix:- A set of numbers arranged in rows and columns so as to form a rectangular array is called…

Q: If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q is also…

A: The matrix is said to be an orthogonal matrix if the product of a matrix and its transpose gives an…

Q: Define Square matrix?

A: A matrix is the arrangement of data in rows and columns.

Q: matrix with eig satisfies

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Q: why is the matrix like that?

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Q: Which of these matrices are lower triangular matrices?

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Q: Define Triangular matrix ?

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Q: A matrix that has the same number of rows as columns is called a/an________ matrix.

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Q: Find an LU-factorization of the matrix.

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Q: What is a gradient Matrix?

A: we have to define a gradient matrix.

Q: 9. When can a square matrix be diagonalized? When can a square matrix be diagonalized orthogonally?

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Q: A row matrix and a column matrix are also called  ______________ .

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Q: How can I find a matrix, given the basis of the null space of said matrix?

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Q: If there is conformability what are the dimensions of the product matrix?

A: let's matrix A and matrix B has dimension as  m×n and n×p respectively then dimension of matrix…

Q: What is the Vandermonde matrix?

A: The Vandermonde method is the most straight-forward method which may be used to find an…

Q: A matrix that is both upper and lower. triangular is called diagonal ylgn ihi

A: Upper and lower triagular matrix

Q: Does Size of a product matrix in Matrix Multiplication matter? explain the suitable size?

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Q: Why is working with orthogonal matrix computationally ecient?

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Q: Which one of the following matrix is a Lower triangular matrix?

A: A triangular matrix is a special kind of square matrix in linear algebra.    Find: Which one of the…

Q: describe how LU factorization of a nonsingular matrix B can be found using Doolittle’s method.

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Q: matrix but not necessarily in natural order is called *       Unit Matrix       Scalar Matrix

A: To name a matrix whose row are the rows of the unit matrix but not necessarily in natural order.…

Q: Explain the mandatory conditions for the addition of two matrices?

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Q: How do you determine the sensitivity for each non zero parameter in this leslie matrix model

A: To determine sensitivity of 2x2 matrix. Let, the 2x2 matrix be a b c d Here,  True positive…

Q: Determine if the matrix is diagonalizable.

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Q: Is it true that Every identity matrix is a diagonal matrix? explain a reason?

A: A square matrix B=[bij] of order n is a diagonal matrix , if all its non-diagonal elements are 0,…

Q: Define Diagonal matrix.

A: Diagonal Matrix: A matrix having all the entries are zero except the diagonal entries is called the…

Q: What is the standard basis of a skew-symmetric matrix?

A: To give the standard basis of a skew-symmetric matrix.

Q: What is a banded matrix and what are the types of these matrices?

A: See the attachment

Q: what is the Dim of a matrix, like if there is Matrix A, what is Dim(A)? Can i have example too?

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Q: 2. for the augmanted matrix

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Q: # Show that diagonally dominated matrices are always invertible. Now, what is a diagonally dominated…

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Q: What is the correct matrix elements

A: Given,            A = 12-1283-18-2310-9151612851014319We know that,        A matrix can be written…

Q: What are the Symmetric Matrices?

A: we know that if transpose of a matrix is equal to itself, then that matrix is said to be symmetric…

Q: singular values and SVD of a n × 1 matrix

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Q: Construct the adjacency matrix. Why is it a block-diagonal matrix?

A: This is always block diagonal matrix in case of bipartite graph.

Q: What is an Inverse matrix?

A: Inverse matrix: If A is a square matrix of order m, and if there exists another square matrix B of…