# Python Program to Display Upper Triangular Matrix

A matrix is a two-dimensional array of many numbers arranged in rows and columns. A square matrix (whose rows and columns has same number of elements) has two diagonals. One is the Primary diagonal - located from the top left corner to the bottom right corner of a square matrix. And the second one is the Secondary diagonal - located from the top right to the bottom left corner.

For a square matrix if all the elements below the Primary diagonal are zero then it is called the Upper Triangular Matrix.

[1, 3, 4]
[0, 5, 6]
[0, 0, 3]


A matrix cannot be converted to the upper triangular matrix if the given matrix is not a square matrix.

## Input Output Scenarios

Assume we have a square matrix. And output matrix will be the upper triangular matrix.

Input matrix:
[1, 3, 5, 7]
[9, 2, 4, 2]
[6, 3, 1, 4]
[5, 8, 7, 6]

Upper triangular matrix:
[1, 3, 5, 7]
[0, 2, 4, 2]
[0, 0, 1, 4]
[0, 0, 0, 6]


Let's see the below examples to display the upper triangular matrix. We will use python list of lists to create matrix.

### Example

In this example we will displayed the upper triangle matrix by replacing lower triangle elements (4, 8, 1) to zero’s.

arr = [[1, 2, 3],
[4, 5, 6],
[1, 8, 5]]

print("The original matrix: ")
for row in arr:
print(row)
print()

print("The upper triangular matrix: ")
if(len(arr) != len(arr)):
print("Matrix should be a square matrix");
else:
for i in range(3):
for j in range(3):
if(i<=j):
print(arr[i][j],end="  ")
else:
print(0,end="  ")
print()


### Output

The original matrix:
[1, 2, 3]
[4, 5, 6]
[1, 8, 5]

The upper triangular matrix:
1  2  3
0  5  6
0  0  5


### Example

In this example we only displayed the upper triangle matrix. Instead of converting lower trying elements to zero’s.

arr = [[1, 2, 3],
[4, 5, 6],
[1, 8, 5]]

print("The original matrix: ")
for row in arr:
print(row)
print()

print("The upper triangular matrix: ")
for i in range(3):
for j in range(3):
if(i > j):
print(end="  ")
else:
print(arr[i][j],end=" ")
print(" ")


### Output

The original matrix:
[1, 2, 3]
[4, 5, 6]
[1, 8, 5]

The upper triangular matrix:
1 2 3
5 6
5


### Example

In this example we will update the original matrix by converting the lower triangle elements to zero, then we will display the upper triangle matrix.

arr = [[1, 2, 3],
[4, 5, 6],
[1, 8, 5]]

print("The original matrix: ")
for row in arr:
print(row)
print()

print("The upper triangular matrix: ")
for i in range(3):
for j in range(3):
if(i > j):
arr[i][j] = 0
print(arr[i][j],end=" ")
else:
print(arr[i][j],end=" ")
print(" ")


### Output

The original matrix:
[1, 2, 3]
[4, 5, 6]
[1, 8, 5]

The upper triangular matrix:
1 2 3
0 5 6
0 0 5


Updated on: 15-May-2023

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