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Matrix Condition NumberThe condition number for matrix inversion with respect to a matrix norm k¢k of a square matrix A is defined by∙(A)=kAkkA¡1k;
if A is non-singular; and ∙(A)=+1 if A is singular.
The condition number is a measure of stability or sensitivity of a matrix (or the linear system it represents) to numerical operations. In other words, we may not be able to trust the results of computations on an ill-conditioned matrix.
Matrices with condition numbers near 1 are said to be well-conditioned. Matrices with condition numbers much greater than one (such as around 105 for a 5£5Hilbert matrix) are said to be ill-conditioned.
If ∙(A) is the condition number of A , then ∙(A) measures a sort of inverse distance from A to the set of singular matrices, normalized by kAk . Precisely, if A isinvertible, and kB¡Ak
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Define bus incidence matrix?
explain bus incidence matrix.
Define sparse matrix?
A matrix that have one or more elements with value zero.
Define inverse of matrix?
From Wolfram MathWorld: The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A-1 such that AA-1=I where I is the identity matrix.
How do you determine if you can multiply two matrices?
Tthe matrix multiplication A*Bis defined only if the number of columns in the first matrix, A, is the same as the number of rows in the second, B. Note that the condition for the multiplication of B*A will be the reverse.
What are elements of a matrix?
They are the number in the matrix.
Define bus incidence matrix?
explain bus incidence matrix.
Define sparse matrix?
A matrix that have one or more elements with value zero.
Define inverse of matrix?
From Wolfram MathWorld: The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A-1 such that AA-1=I where I is the identity matrix.
How i define Efficiency of human nature?
The Matrix.
Define an indempotent matrix?
The phrase "idempotent matrix" is an algebraic term. It is defined as a matrix that equals itself when multiplied by itself.
How do you determine if you can multiply two matrices?
Tthe matrix multiplication A*Bis defined only if the number of columns in the first matrix, A, is the same as the number of rows in the second, B. Note that the condition for the multiplication of B*A will be the reverse.
Each number in a matrix is called a?
Each number in the matrix is called an element of the matrix
How do you generate generator matrix in linear block code when a code word is given?
The generator matrix is made out of that code word and all the possibilities for the code words. The number of rows of the generator matrix are the number of message bits and the number of columns are equal to the total number of bits i.e parity bits + message bits. The only necessary condition is that each row of generator matrix is linearly independent of the other row.
What are elements of a matrix?
They are the number in the matrix.
What is a matrix with the same number of rows as columns?
A matrix having the same number of rows and columns is a SQUARE MATRIX.
What is each number that you find in a matrix?
Each number in a matrix is called an element.
What is the significance of the maximal eigenvalue in the context of matrix analysis and how does it impact the overall properties of the matrix?
The maximal eigenvalue of a matrix is important in matrix analysis because it represents the largest scalar by which an eigenvector is scaled when multiplied by the matrix. This value can provide insights into the stability, convergence, and behavior of the matrix in various mathematical and scientific applications. Additionally, the maximal eigenvalue can impact the overall properties of the matrix, such as its spectral radius, condition number, and stability in numerical computations.
