Final answer:
The row-sum norm of a matrix is the maximum absolute row sum and the column-sum norm is the maximum sum of the absolute column values.
Step-by-step explanation:
To find the row-sum norm (also known as the infinity norm) of a matrix, you must determine the maximum absolute row sum of the matrix. For every row, you add up the absolute values of the elements in that row. The row-sum norm is the largest sum obtained from all rows. On the other hand, to find the column-sum norm (also known as the 1-norm) of a matrix, you calculate the sum of the absolute values of each column and then take the maximum sum among all columns.
Example Calculation of Row-Sum and Column-Sum Norms
Consider the matrix:
A =
[2 -3]
[5 1]
For row-sum norm:
The maximum value is 6, so the row-sum norm is 6.
For column-sum norm:
The maximum value is 7, so the column-sum norm is 7.