{"id":20179,"date":"2021-09-06T13:42:03","date_gmt":"2021-09-06T08:12:03","guid":{"rendered":"https:\/\/python-programs.com\/?p=20179"},"modified":"2021-11-22T18:36:25","modified_gmt":"2021-11-22T13:06:25","slug":"python-program-to-find-the-sum-of-a-lower-triangular-matrix","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-to-find-the-sum-of-a-lower-triangular-matrix\/","title":{"rendered":"Python Program to Find the Sum of a Lower Triangular Matrix"},"content":{"rendered":"<p>In the previous article, we have discussed <a href=\"https:\/\/python-programs.com\/python-program-to-find-the-sum-of-an-upper-triangular-matrix\/\">Python Program to Find the Sum of an Upper Triangular Matrix<\/a><\/p>\n<p>Given a matrix and the task is to find the sum of the lower triangular matrix of the given matrix in Python.<\/p>\n<p><strong>What is a matrix:<\/strong><\/p>\n<p>A matrix is a rectangular sequence of numbers divided into columns and rows. A matrix element or entry is a number that appears in a matrix.<\/p>\n<p><strong>Example:<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-7021 aligncenter\" src=\"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/05\/matrix.jpg\" alt=\"\" width=\"561\" height=\"426\" srcset=\"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/05\/matrix.jpg 561w, https:\/\/python-programs.com\/wp-content\/uploads\/2021\/05\/matrix-300x228.jpg 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Above is the matrix which contains 5 rows and 4 columns and having elements from 1 to 20.<\/p>\n<p>In this order, the dimensions of a matrix indicate the number of rows and columns.<\/p>\n<p>Here as there are 5 rows and 4 columns it is called a 5*4 matrix.<\/p>\n<p><strong>Lower Triangular Matrix:<\/strong><\/p>\n<p>A lower triangular matrix is one that has all of its upper triangular elements equal to zero. In other words, all non-zero elements are on the main diagonal or in the lower triangle.<\/p>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given Matix :\r\n1 6 4 \r\n8 1 3\r\n1 6 2<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The sum of Lower Triangular matrix of the given matrix is :\r\n13<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given Matix :\r\n7 9 \r\n3 6<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>The sum of Lower Triangular matrix of the given matrix is :\r\n9<\/pre>\n<h2>Program to Find the Sum of a Lower Triangular Matrix in Python<\/h2>\n<p>Below are the ways to find the sum of the lower triangular matrix of the given matrix in Python.<\/p>\n<ul>\n<li><a href=\"#Using_For_Loop_(Static_Input)\">Using For Loop (Static Input)<\/a><\/li>\n<li><a href=\"#Using_For_loop_(User_Input)\">Using For loop (User Input)<\/a><\/li>\n<\/ul>\n<h3 id=\"Using_For_Loop_(Static_Input)\">Method #1: Using For Loop (Static Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the matrix as static input and store it in a variable.<\/li>\n<li>Calculate the number of rows of the given matrix by calculating the length of the nested list using the len() function and store it in a variable mtrxrows.<\/li>\n<li>Calculate the number of columns of the given matrix by calculating the length of the first list in the nested list using the len() function and store it in a variable mtrxcolums.<\/li>\n<li>Take a variable say <strong>lower_sum <\/strong>and initialize its value to 0.<\/li>\n<li>Loop till the given number of rows using the For loop.<\/li>\n<li>Inside the For loop, Iterate till the given number of columns using another Nested For loop(Inner For loop).<\/li>\n<li>Check if the condition n is less than m using the if conditional statement where n is the iterator value of the parent For loop and m is the iterator value of the inner For loop.<\/li>\n<li>If the statement is true, add the gvnmatrix[n][m] to the above-initialized <strong>lower_sum\u00a0<\/strong>and store it in the same variable <strong>lower_sum.<\/strong><\/li>\n<li>Print the variable <strong>lower_sum\u00a0<\/strong>to get the sum of the lower triangular matrix of the given matrix.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Give the matrix as static input and store it in a variable.\r\nmtrx = [[1, 6, 4], [8, 1, 3], [1, 6, 2]]\r\n# Calculate the number of rows of the given matrix by\r\n# calculating the length of the nested list using the len() function\r\n# and store it in a variable mtrxrows.\r\nmtrxrows = len(mtrx)\r\n# Calculate the number of columns of the given matrix by\r\n# calculating the length of the first list in the nested list\r\n# using the len() function and store it in a variable mtrxcols.\r\nmtrxcols = len(mtrx[0])\r\nprint(\"The sum of Lower Triangular matrix of the given matrix is :\")\r\n# Take a variable say lower_sum and initialize its value to 0.\r\nlower_sum = 0\r\n# To print all the elements of the given matrix.\r\n# Loop till the given number of rows using the For loop.\r\nfor n in range(mtrxrows):\r\n        # Inside the For loop, Iterate till the given number of columns using another\r\n        # Nested For loop(Inner For loop).\r\n    for m in range(mtrxcols):\r\n      # Check if the condition n is less than m using the if conditional statement where n\r\n      # is the iterator value of the parent For loop and m is the iterator value of the\r\n      # inner For loop.\r\n        if n &lt; m:\r\n          # If the statement is true, add the gvnmatrix[n][m] to the above-initialized\r\n          # lower_sum\u00a0and store it in the same variable lower_sum.\r\n            lower_sum += mtrx[n][m]\r\n# Print the variable lower_sum\u00a0to get the sum of the lower triangular matrix of the\r\n# given matrix.\r\nprint(lower_sum)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The sum of Lower Triangular matrix of the given matrix is :\r\n13<\/pre>\n<h3 id=\"Using_For_loop_(User_Input)\">Method #2: Using For loop (User Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the number of rows of the matrix as user input using the int(input()) function and store it in a variable.<\/li>\n<li>Give the number of columns of the matrix as user input using the int(input()) function and store it in another variable.<\/li>\n<li>Take a list and initialize it with an empty value using [] or list() to say\u00a0<strong>gvnmatrix<\/strong>.<\/li>\n<li>Loop till the given number of rows using the For loop<\/li>\n<li>Inside the For loop, Give all the row elements of the given Matrix as a list using the list(),map(),int(),split() functions and store it in a variable.<\/li>\n<li>Add the above row elements list to\u00a0<strong>gvnmatrix<\/strong>\u00a0using the append() function.<\/li>\n<li>Take a variable say <strong>lower_sum <\/strong>and initialize its value to 0.<\/li>\n<li>Loop till the given number of rows using the For loop.<\/li>\n<li>Inside the For loop, Iterate till the given number of columns using another Nested For loop(Inner For loop).<\/li>\n<li>Check if the condition n is less than m using the if conditional statement where n is the iterator value of the parent For loop and m is the iterator value of the inner For loop.<\/li>\n<li>If the statement is true, add the gvnmatrix[n][m] to the above-initialized <strong>lower_sum\u00a0<\/strong>and store it in the same variable <strong>lower_sum.<\/strong><\/li>\n<li>Print the variable <strong>lower_sum\u00a0<\/strong>to get the sum of the lower triangular matrix of the given matrix.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Give the number of rows of the matrix as user input using the int(input()) function\r\n# and store it in a variable.\r\nmtrxrows = int(input('Enter some random number of rows of the matrix = '))\r\n# Give the number of columns of the matrix as user input using the int(input()) function\r\n# and store it in another variable.\r\nmtrxcols = int(input('Enter some random number of columns of the matrix = '))\r\n# Take a list and initialize it with an empty value using [] or list() to say gvnmatrix.\r\nmtrx = []\r\n# Loop till the given number of rows using the For loop\r\nfor n in range(mtrxrows):\r\n    # Inside the For loop, Give all the row elements of the given Matrix as a list using\r\n    # the list(),map(),int(),split() functions and store it in a variable.\r\n    l = list(map(int, input(\r\n        'Enter {'+str(mtrxcols)+'} elements of row {'+str(n+1)+'} separated by spaces = ').split()))\r\n    # Add the above row elements list to gvnmatrix using the append() function.\r\n\r\n    mtrx.append(l)\r\n    \r\nprint(\"The sum of Lower Triangular matrix of the given matrix is :\")\r\n# Take a variable say lower_sum and initialize its value to 0.\r\nlower_sum = 0\r\n# To print all the elements of the given matrix.\r\n# Loop till the given number of rows using the For loop.\r\nfor n in range(mtrxrows):\r\n        # Inside the For loop, Iterate till the given number of columns using another\r\n        # Nested For loop(Inner For loop).\r\n    for m in range(mtrxcols):\r\n      # Check if the condition n is less than m using the if conditional statement where n\r\n      # is the iterator value of the parent For loop and m is the iterator value of the\r\n      # inner For loop.\r\n        if n &lt; m:\r\n          # If the statement is true, add the gvnmatrix[n][m] to the above-initialized\r\n          # lower_sum\u00a0and store it in the same variable lower_sum.\r\n            lower_sum += mtrx[n][m]\r\n# Print the variable lower_sum\u00a0to get the sum of the lower triangular matrix of the\r\n# given matrix.\r\nprint(lower_sum)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some random number of rows of the matrix = 2\r\nEnter some random number of columns of the matrix = 2\r\nEnter {2} elements of row {1} separated by spaces = 7 9\r\nEnter {2} elements of row {2} separated by spaces = 3 6\r\nThe sum of Lower Triangular matrix of the given matrix is :\r\n9<\/pre>\n<p>Enhance your coding skills with our list of <a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Python Basic Programs<\/a> provided and become a pro in the general-purpose programming language Python in no time.<\/p>\n<ul>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-check-whether-a-matrix-is-a-scalar-or-not\/\">Python Program to Check Whether a Matrix is a Scalar or Not<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-check-two-matrix-are-equal-or-not\/\">Python Program to Check Two Matrix are Equal or Not<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-the-normal-and-trace-of-a-matrix\/\"><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Python Program to find the Normal and Trace of a Matrix&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4224,&quot;10&quot;:2,&quot;15&quot;:&quot;Arial&quot;}\">Python Program to find the Normal and Trace of a Matrix<\/span><\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-for-sum-of-middle-row-and-column-in-matrix\/\">Python Program for Sum of Middle Row and Column in Matrix<\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In the previous article, we have discussed Python Program to Find the Sum of an Upper Triangular Matrix Given a matrix and the task is to find the sum of the lower triangular matrix of the given matrix in Python. What is a matrix: A matrix is a rectangular sequence of numbers divided into columns &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-to-find-the-sum-of-a-lower-triangular-matrix\/\"> <span class=\"screen-reader-text\">Python Program to Find the Sum of a Lower Triangular Matrix<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":20209,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true},"categories":[5],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v18.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python Program to Find the Sum of a Lower Triangular Matrix - Python Programs<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/python-programs.com\/python-program-to-find-the-sum-of-a-lower-triangular-matrix\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python Program to Find the Sum of a Lower Triangular Matrix - Python Programs\" \/>\n<meta property=\"og:description\" content=\"In the previous article, we have discussed Python Program to Find the Sum of an Upper Triangular Matrix Given a matrix and the task is to find the sum of the lower triangular matrix of the given matrix in Python. 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