The square of a matrix

What you need:

• paper
• Pen

The multiplication of a matrix by itself

• For arithmetic operations with Matrices special rules apply. So it is not enough to form the squares of the individual elements to get the square of the matrix.
• In general, you can multiply two matrices together if the number of columns in the first corresponds to the number of rows in the second matrix. Since a matrix to be squared is multiplied by itself, the number of rows must match the number of columns. If this requirement is not met, you cannot determine the square of the matrix.
• Falk's scheme, which you can also use to calculate the square of a matrix, has proven itself for the multiplication of matrices.
• Matrices are identified by capital letters. The square of the matrix A is therefore A.².

How to find the square according to Falk's scheme

1. Divide your writing area into four sections with a vertical and a horizontal line. Write the matrix once in the upper right and once in the lower left section.


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2. In the lower right area you develop the square of the matrix, which in turn is a matrix. You have to perform several multiplications for each field of the result matrix and add the results. Always include the row and column in the calculations that are assigned to the respective field. You can see which these are with the help of the diagram that has been written down.
3. For the field in the first row and column of the result matrix, first multiply the first value in the first row by the first value in the first column, i.e. by yourself. Then multiply the second value of the first row by the second value of the first column, the third value of the first row with the third value of the first column and so on, depending on how many rows and columns the matrix is Has. Add up all of these products and enter the result in the result field.
4. Now determine the value for the field in the first row and second column of the result matrix. To do this, multiply the first value in the first row by the first value in the second column, then the second value in the first row by the second Value of the second column, then the third value of the first row, then the third value of the second column, and so on, and then add these results together again.
5. Apply this principle to all fields of the result matrix. You always multiply the values ​​of the row belonging to the field with those of the corresponding column one after the other and add the results.