MATHEMATICA HOW TO

# How to | Update Parts of a Matrix

Mathematica has many matrix operations that support operations such as building, computing, and visualizing matrices. It also has a rich language for picking out parts of matrices and assigning new values to them.

Define the following matrix:

 Out[2]//MatrixForm=

Use (the short form of Part) on the left-hand side of an assignment to set an element:

 Out[3]=

This shows that the element at position (1, 2) has been updated:

 Out[4]//MatrixForm=

To set an entire row, use one index to specify the row and assign it to the new row:

 Out[6]//MatrixForm=

To set an entire column, select all rows with All and specify the column:

 Out[8]//MatrixForm=

To set a submatrix you can use the short form of Span ().

First set up a 5×5 matrix of random integers between 0 and 10:

 Out[25]//MatrixForm=

The top-left 3×4 matrix highlighted here corresponds to rows 1 through 3 and columns 1 through 4:

 Out[49]=

Update the highlighted submatrix by using the short form of Span () to specify the relevant span of rows and columns:

 Out[27]//MatrixForm=

Update all elements except the outermost rows and columns (negative indices count from the end):

 Out[29]//MatrixForm=

When you update a large matrix you should try to avoid doing this in a loop. If you can use one of the updating techniques to update all elements in one command, this will typically be much faster:

This is a slow way to update every element in a row:

 Out[37]=

This is much faster:

 Out[38]=

If you cannot avoid updating a matrix in a loop, you need to take care to avoid extra references to the matrix. Otherwise the matrix will be copied and the loop will not run very fast:

This takes care to avoid extra references. The loop runs quite fast:

 Out[40]=

This makes a copy of the matrix at every step, and the loop does not run very fast:

 Out[41]=

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