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Is that the determinant of any matrix is equal to the product of their eigenvalues?
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What does determine mean in maths?
In Algebra, the word determinant is a special number which is associated to any square matrix. Like for example, a rectangular array of numbers where the finite number of rows and columns are equal. Therefore, the meaning of a determinant is a scale factor for measuring wherever the matrix is regarded.
What is the difference between matrices and determinants?
Both matrix and determinants are the part of business mathematics. Both are useful for solving business problem. Both are helpful for calculation of each other. For calculation of inverse of matrix, we need to calculate the determinant. For calculating the value of 3X3 matrix or more matrix, we need to divide determinants in sub-matrix. but there are many differences between matrix and determinants which we can explain in following points. 1. Matrix is the set of numbers which are covered by two brackets. Determinants is also set of numbers but it is covered by two bars. 2. It is not necessary that number of rows will be equal to the number of columns in matrix. But it is necessary that number of rows will be equal to the number of columns in determinant. 3. Matrix can be used for adding, subtracting and multiplying the coefficients. Determinant can be used for calculating the value of x, y and z with Cramer's Rule. By Er. Hafijullah
What is harmitian matrix?
Hermitian matrix (please note spelling): a square matrix with complex elements that is equal to its conjugate transpose.
What are the following terms- eignvalues of matrix-entries of matrix-equality of matrix-matrix of groups-identity of matrix-inverse matrix-multiplication of matrices?
First, a small note: an m-by-n or m x n matrix has m rows and n columns.The eigenvalues λ of a matrix A are scalars such that Ax = λx for some nonzero x vector.The entries aij of a matrix A are the numbers contained within the matrix, each with a unique position of the ith row and jth column.'Equality' in matrices has the same definition as for the rest of mathematics.A matrix of groups is a matrix whose entries are members of a group, often with specific entries in certain positions.The matrix identity In is that square n by n matrix whose entries aij are 1 if i = j, and 0 if i ≠j.The inverse of a square matrix A is the square matrix B such that AB = In, denoted by B = A-1.Matrix multiplication is the act of combining two matrices, the p-by-q A = (aij) and the q-by-r B = (bij) to form the new matrix p-by-r C = (cij) such that cij = Σaikbkj, where 1 ≤ k ≤ q. This is denoted by C = AB. Note that matrix mulplication is not commutative, i.e. AB does not necessarily equal BA; the order of the components is important and must be maintained to achieve the result. Note also that although p does not need to equal r, q must be the same in each matrix.
If rank of the matrix is equal to no of variable then it have?
Then it has (not have!) a unique solution.
Why only square matrix have determinant?
The square matrix have determinant because they have equal numbers of rows and columns. <<>> Determinants are not defined for non-square matrices because there are no applications of non-square matrices that require determinants to be used.
What does determine mean in maths?
In Algebra, the word determinant is a special number which is associated to any square matrix. Like for example, a rectangular array of numbers where the finite number of rows and columns are equal. Therefore, the meaning of a determinant is a scale factor for measuring wherever the matrix is regarded.
What is the difference between matrices and determinants?
Both matrix and determinants are the part of business mathematics. Both are useful for solving business problem. Both are helpful for calculation of each other. For calculation of inverse of matrix, we need to calculate the determinant. For calculating the value of 3X3 matrix or more matrix, we need to divide determinants in sub-matrix. but there are many differences between matrix and determinants which we can explain in following points. 1. Matrix is the set of numbers which are covered by two brackets. Determinants is also set of numbers but it is covered by two bars. 2. It is not necessary that number of rows will be equal to the number of columns in matrix. But it is necessary that number of rows will be equal to the number of columns in determinant. 3. Matrix can be used for adding, subtracting and multiplying the coefficients. Determinant can be used for calculating the value of x, y and z with Cramer's Rule. By Er. Hafijullah
Can a 3 by 3 matrix equal zero?
First we need to ask what you mean by a matrix equalling a number? A matrix is a rectangular array of numbers all of which might be zero and this is called the zero matrix. We can take the determinant of a square matrix such as a 3x3 and this may be zero even without the entries being zero.
What is a symmetric matrix?
a square matrix that is equal to its transpose
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.
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.
What shows objects arrangged in equal rows and columns?
This is a square matrix where the number of rows and the number of columns are equal.
What is scalene matrix?
A square matrix is said to be scalene Matrix if it has all principal diagonal elements equal and remaining all
What is harmitian matrix?
Hermitian matrix (please note spelling): a square matrix with complex elements that is equal to its conjugate transpose.
What is the definition of a Hermitian matrix?
Hermitian matrix defined:If a square matrix, A, is equal to its conjugate transpose, A†, then A is a Hermitian matrix.Notes:1. The main diagonal elements of a Hermitian matrix must be real.2. The cross elements of a Hermitian matrix are complex numbers having equal real part values, and equal-in-magnitude-but-opposite-in-sign imaginary parts.
The rank of product of two matrices cannot exceed the rank of either factor?
The statement that the rank of product of two matrices cannot exceed the rank of either factor is a true statement. The rank of a matrix is the largest number of linearly independent rows or columns. The column rank is equal to the row rank in every matrix.
