[PDF] condition number for matrix multiplication

2 nov. 2013 · Given two square matrices A and B, is the following inequality cond(AB)?cond(A)cond(B),. where cond is the condition number, true? Is this  Condition Number and Sensitivity of Matrix-Vector MultiplicationCondition number matrix matrix multiplicationCondition number of a matrix-vector productlinear algebra - Matrix condition number and loss of accuracyAutres résultats sur math.stackexchange.comQuestions d'autres utilisateurs
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  • What is the condition for matrix multiplication?

    Matrix multiplication Condition
    To perform multiplication of two matrices, we should make sure that the number of columns in the 1st matrix is equal to the rows in the 2nd matrix.
    Therefore, the resulting matrix product will have a number of rows of the 1st matrix and a number of columns of the 2nd matrix.

  • What are the conditions for matrix addition and multiplication?

    Consider two matrices A & B.
    These matrices can be added if (if and only if) the order of the matrices are equal, i.e. the two matrices have the same number of rows and columns.
    For example, say matrix A is of the order 3 × 4, then the matrix B can be added to matrix A if the order of B is also 3 × 4.

  • What is a good condition number for a matrix?

    Condition number depends on the underlying norm.
    However, regardless of the norm, it is always greater or equal to 1.
    If it is close to one, the matrix is well conditioned which means its inverse can be computed with good accuracy.

  • What is a good condition number for a matrix?

    How to find the condition number of a matrix?

    1Choose a matrix norm.
    Although the choice is problem-dependent, the matrix 2-norm is typically used.    2Evaluate the inverse of A. 3Calculate ? A ? \\Vert A\\Vert ?A? and ? A ? 1 ? \\Vert A^{-1}\\Vert ?A?1?. 4Multiply the norms to find cond(A).

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