1. A Color (picture) is worth 1000 words
Dafna Minster
July 2012

2. introduction
Matrices have many uses in mathematics and computer science. Matrices allow storage of large amount of information regarding variables and also allow methods that define operations upon themselves.   Students who are learning the subject of matrices have some difficulties. One difficulty is: understanding the ways of scanning the matrix. The difficulty lies within the fact that a nested loop (loop inside a loop) is required. Other problems include scanning the matrix' diagonals and all items above/bellow the diagonals. One operation that is especially difficult is to transpose – to swap between rows and columns.   This tip shows visual methods on how to scan a matrix step by step. The first part of the tip will shows the outer loop by coloring the rows, and the second part will describe the inner loop by using a different color.   This tip will help teachers to better convey the subject matrices using a graphical approach.   As said in the title: A Color (picture) is worth 1000 words.
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Dafna Minster

3. Matrix - rows Start row for ( int i = 0 ; i < matrix.length ; i++ )
End row
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4. Matrix - columns Start column End column
for ( int i = 0 ; i < matrix.length ; i++ )
for ( int j = 0 ; j < matrix[i].length ; j++ )
command ( matrix [ i ] [ j ] );
End column
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5. Matrix – main diagonal for ( int i = 0 ; i < matrix.length ; i++ )
command ( matrix [ i ] [ i ] ) ;
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6. Matrix – secondary diagonal
for ( int i = 0 ; i < matrix.length ; i++ )
command(matrix[i] [matrix.length-1-i]);
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7. Matrix – above main diagonal
j = i +1
j = i
j = i -1
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8. Matrix – above main diagonal
j = i +1
j = i
j = i -1
Start row
for ( int i = 0 ; i < matrix.length - 1 ; i++ )
End row
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9. Matrix – above main diagonal
j = i +1
Start column
j = i
j = i -1
for ( int i = 0 ; i < matrix.length - 1 ; i++ )
for ( int j = i +1 ; j < matrix[i].length ; j++ )
command ( matrix [ i ] [ j ] );
End column

10. Matrix – Below main diagonal
j = i +1
j = i
j = i -1
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11. Matrix – Below main diagonal
j = i +1
j = i
j = i -1
Start row
for ( int i = 1 ; i < matrix.length ; i++ )
End row

12. Matrix – Below main diagonal
End column
j = i +1
j = i
j = i -1
for ( int i = 1 ; i < matrix.length ; i++ )
for ( int j = 0 ; j < i ; j++ )
command ( matrix [ i ] [ j ] ) ;
Start column

13. Matrix – above secondary diagonal
j = matrix[i].length - 1- i
j = matrix[i].length - i
j = matrix[i].length - 2- i
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14. Matrix – above secondary diagonal
j = matrix[i].length - 1- i
j = matrix[i].length - 2- i
Start row
for ( int i = 0 ; i < matrix.length - 1 ; i++ )
End row
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15. Matrix – above secondary diagonal
j = matrix[i].length - 1- i
j = matrix[i].length - 2- i
End column
for ( int i = 0 ; i < matrix.length - 1 ; i++ )
for ( int j = 0; j < matrix[i].length - 1- i ; j++)
command (matrix[i] j]);
Start column

16. Matrix – Below secondary diagonal
j = matrix[i].length - 1- i
j = matrix[i].length - i
j = matrix[i].length - 2- i
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17. Matrix – below secondary diagonal
j = matrix[i].length - 1- i
j = matrix[i].length - i
Start row
for ( int i = 1 ; i < matrix.length ; i++ )
End row
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18. Matrix – above secondary diagonal
j = matrix[i].length - 1- i
j = matrix[i].length - i
Start column
for ( int i = 1 ; i < matrix.length ; i++ )
for ( int j = matrix[i].length - i ;
j < matrix[i].length ; j++)
command (matrix[ i ] [ j ]);
End column

19. The end
Dafna Minster
July 2012
All rights reserved to Dafna Minster