what is a Hermitian matrix? does every Hermitian matrix has to be square matrices?

Q: Can you provide one image or figure of the hermitian 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: must be a non-invertible matrix.

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Q: What is a matrix?

A: Definition :                           A rectangular array of m × n numbers ( real or…

Q: Determine whether the matrix is orthogonally diagonalizable.

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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: Is it possible for A3 to be an identity matrix without A beinginvertible? Explain.

A: To explain:It is possible for A3 to be an identity matrix without A being invertible.By definition

Q: Is every diagonal matrix a scalar matrix? Explain.

A: We have to explain that every diagonal matrix a scalar matrix. We know that diagonal matrices are…

Q: If S = A + iB is a Hermitian matrix, are its real and imaginary parts symmetric?

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Q: Under which conditions an inverse matrix be defined for a matrix?

A: There are two conditions for matrix to be invertible.

Q: Is the matrix diagonalizable? If yes, find diagonal matrix D and regular matrix P such that AP = PD.…

A: Yes, Given Matrix is diagnolizable.

Q: State whether the matrix is diagonalizable or not. [::] diagonalizable O not diagonalizable

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Q: Why is it important that the matrix is invertible? Give and example.

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Q: Consider the matrix

A: Given, the matrix                A=0-3-1020233 And the eigenvalues of A are λ=1, and λ=2.

Q: Give an example of two matrices A and B such that BA exists, but AB is undefined. Explain why your…

A: Finding the product of two matrices is only possible when the inner dimensions are the same, meaning…

Q: Prove that if an upper triangular matrix is orthogonal, then it must be a diagonal matrix

A: Solution: If the multiplication of matrix with its transpose is equal to the identity, then a matrix…

Q: Explain why the matrix is not diagonalizable.

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Q: 2 0 -1 2 0 0 1 1

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Q: Is a singular matrix consistent/inconsistent? Is a nonsingular matrix consistent/inconsistent?

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Q: Construct a 2 x 2 matrix that is diagonalizable but not invertible.

A: we have to construct a 2 x 2 matrix that is diagonalizable but not invertible.

Q: Let A and B be two square Matrices of the same Size such that A is not invertible (B may or not be…

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Q: An n x n matrix that is orthogonally diagonalizable must be symmetric.

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Q: What is a Augmented Matrix?

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Q: Show that the matrix is not diagonalizable.

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Q: How do you know whether a matrix is invertible?

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Q: Show that every diagonalizable matrix has a square root.

A: Square Root Matrix of a Diagonalizable Matrix is Diagonalizable. A is diagonalizable. Therefore,…

Q: A diagonal matrix is a square matrix that if rotated to give the original matrix 1- right 2-Error

A: a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term…

Q: The product of two invertible matrices is always non-zero. Select one: OTrue

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Q: • Is it possible for a 5 x 5 matrix to be invertible when its columns do not span R°? Why or why…

A: According to the Invertible matrix theorem, the matrix with n x n order cannot be invertible if its…

Q: What type of matrix is a linear combination of scalar ma- trices? Justify your answer.

A: Consider n scalar matrices with each matrix in k×k order: A1, A2, A3, ⋯, An Also, let b1, b2, b3, ⋯,…

Q: Write a second degree equation matrix and prove that it is in vector space?

A: To show: An example of a second-degree equation matrix which is in vector space.

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

A: The commutative property of matrices can be stated as . The matrix obtained by interchanging the…

Q: Show that the matrix below does not have an LU-factorization.

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Q: Which matrix is not similar to

A: Given that Matrix- X= 011112-12114, A=21-121011114,B=01111411-122, C=0-111-12121-14, D=100030003,…

Q: Is the sum of two invertible matrices invertible? Explain why or why not. Illustrate your conclusion…

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Q: Show that the diagonal entries of a Hermitian matrix must be real.

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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: Find a family of the matrices that is similar to the matrix

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Q: Determine if the matrix is diagonalizable.

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Q: Can arrowhead matrix be similar to a tridiagonal matrix?

A: An arrowhead matrix is one that is a square matrix with zero entries everywhere except on the…

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

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

Q: Is every scalar matrix nonsingular? Explain.

A: Query- Is every scalar matrix nonsingular? Explain. Answer-  A non-singular matrix is a square one…

Q: Show that a triangular matrix is normal if it is diagonal

A: Given: A triangular matrix is normal.if it is diagonal

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: Construct a nonzero 2 × 2 matrix that is invertible but not diagonalizable.

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Q: Determine whether the matrix B = is awesome or not. %3D

A: 7.1 To determine whether the matrix B is awesome or not. Where  B=i2−3232−i2and B is awesome if…

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…

Q: What is a column matrix?

A: Definition of column matrix – A vector which is represented with a list of number is called a column…