{"id":20290,"date":"2021-09-09T19:57:45","date_gmt":"2021-09-09T14:27:45","guid":{"rendered":"https:\/\/python-programs.com\/?p=20290"},"modified":"2021-11-22T18:36:23","modified_gmt":"2021-11-22T13:06:23","slug":"python-program-to-find-the-normal-and-trace-of-a-matrix","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-to-find-the-normal-and-trace-of-a-matrix\/","title":{"rendered":"Python Program to find the Normal and Trace of a Matrix"},"content":{"rendered":"<p>In the previous article, we have discussed <a href=\"https:\/\/python-programs.com\/python-program-to-print-odd-numbers-in-given-range-using-recursion\/\">Python Program to Print Odd Numbers in Given Range Using Recursion<\/a><\/p>\n<p>Given a matrix and the task is to find the normal and trace 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>Normal of a matrix:<\/strong><\/p>\n<p>The sum of squares is normal for all the matrix entries.<\/p>\n<p><strong>Trace of a matrix:<\/strong><\/p>\n<p>Trace is the sum of the Matrix&#8217;s diagonal parts.<\/p>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given Matix :\r\n2 6 4 \r\n8 5 3 \r\n1 6 8<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The trace value of the given matrix is : 15\r\nThe normal value of the given matrix is : 6.557438524302<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given Matix : \r\n1 2 3 4\r\n7 5 8 6\r\n9 4 2 5\r\n1 1 1 1<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>The trace value of the given matrix is : 9\r\nThe normal value of the given matrix is : 7.745966692414834<\/pre>\n<h2>Program to find the Normal and Trace of a Matrix in Python<\/h2>\n<p>Below are the ways to find the normal and trace 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>Import the math module using the import keyword.<\/li>\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 <strong>mtrxrows<\/strong>.<\/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 <strong>mtrxcolums<\/strong>.<\/li>\n<li>Take a variable say <strong>mtrxtrace<\/strong> which stores the trace of the given matrix and initialize its value to 0.<\/li>\n<li>Take a variable say <strong>mtrxsum<\/strong> which stores the sum of all elements of the matrix 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 parent loop iterator value is equal to the inner loop iterator value using the if conditional statement(This is whether the element is diagonal element or not)<\/li>\n<li>If it is true then add this value to <strong>mtrxtrace.<\/strong><\/li>\n<li>After the if conditional statement, Add the gvnmatrix[n][m] to the above-initialized <strong>mtrxsum <\/strong>and store it in the same variable <strong>mtrxsum.<\/strong><\/li>\n<li>After the end of two loops calculate the square root of the <strong>mtrxsum\u00a0<\/strong>value using the sqrt() function and store this result in <strong>mtrxnormal<\/strong> variable.<\/li>\n<li>Print the value of <strong>mtrxtrace<\/strong> which gives the value of the trace of the given matrix.<\/li>\n<li>Print the value of <strong>mtrxnormal <\/strong>which gives the value of the normal 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\"># Import the math module using the import keyword.\r\nimport math\r\n# Give the matrix as static input and store it in a variable.\r\nmtrx = [[2, 6, 4], [8, 5, 3], [1, 6, 8]]\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\n# Take a variable say mtrxtrace which stores the trace of the given matrix\r\n# and initialize its value to 0.\r\nmtrxtrace = 0\r\n# Take a variable say mtrxsum which stores the sum of all elements of the matrix\r\n# and initialize its value to 0.\r\nmtrxsum = 0\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 parent loop iterator value is equal to the inner loop iterator value\r\n        # using the if conditional statement\r\n        # (This is whether the element is diagonal element or not)\r\n        if(n == m):\r\n            # If it is true then add this value to mtrxtrace.\r\n            mtrxtrace = mtrxtrace+mtrx[n][m]\r\n\r\n        # After the if conditional statement,\r\n        # Add the gvnmatrix[n][m] to the above-initialized mtrxsum\r\n        # and store it in the same variable mtrxsum.\r\n        mtrxsum = mtrxsum+mtrx[n][m]\r\n# After the end of two loops calculate the square root of the mtrxsum\u00a0value\r\n# using the sqrt() function\r\n# and store this result in mtrxnormal variable.\r\nmtrxnormal = math.sqrt(mtrxsum)\r\n# Print the value of mtrxtrace which gives the value of the trace of the given matrix.\r\nprint('The trace value of the given matrix is :', mtrxtrace)\r\n# Print the value of mtrxnormal which gives the value of the normal of the given matrix.\r\nprint('The normal value of the given matrix is :', mtrxnormal)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The trace value of the given matrix is : 15\r\nThe normal value of the given matrix is : 6.557438524302<\/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>Import the math module using the import keyword.<\/li>\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>mtrxtrace<\/strong> which stores the trace of the given matrix and initialize its value to 0.<\/li>\n<li>Take a variable say <strong>mtrxsum<\/strong> which stores the sum of all elements of the matrix 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 parent loop iterator value is equal to the inner loop iterator value using the if conditional statement(This is whether the element is diagonal element or not)<\/li>\n<li>If it is true then add this value to <strong>mtrxtrace.<\/strong><\/li>\n<li>After the if conditional statement, Add the gvnmatrix[n][m] to the above-initialized <strong>mtrxsum <\/strong>and store it in the same variable <strong>mtrxsum.<\/strong><\/li>\n<li>After the end of two loops calculate the square root of the <strong>mtrxsum\u00a0<\/strong>value using the sqrt() function and store this result in <strong>mtrxnormal<\/strong> variable.<\/li>\n<li>Print the value of <strong>mtrxtrace<\/strong> which gives the value of the trace of the given matrix.<\/li>\n<li>Print the value of <strong>mtrxnormal <\/strong>which gives the value of the normal 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\"># Import the math module using the import keyword.\r\nimport math\r\n# 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    mtrx.append(l)\r\n# Take a variable say mtrxtrace which stores the trace of the given matrix\r\n# and initialize its value to 0.\r\nmtrxtrace = 0\r\n# Take a variable say mtrxsum which stores the sum of all elements of the matrix\r\n# and initialize its value to 0.\r\nmtrxsum = 0\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 parent loop iterator value is equal to the inner loop iterator value\r\n        # using the if conditional statement\r\n        # (This is whether the element is diagonal element or not)\r\n        if(n == m):\r\n            # If it is true then add this value to mtrxtrace.\r\n            mtrxtrace = mtrxtrace+mtrx[n][m]\r\n\r\n        # After the if conditional statement,\r\n        # Add the gvnmatrix[n][m] to the above-initialized mtrxsum\r\n        # and store it in the same variable mtrxsum.\r\n        mtrxsum = mtrxsum+mtrx[n][m]\r\n# After the end of two loops calculate the square root of the mtrxsum\u00a0value\r\n# using the sqrt() function\r\n# and store this result in mtrxnormal variable.\r\nmtrxnormal = math.sqrt(mtrxsum)\r\n# Print the value of mtrxtrace which gives the value of the trace of the given matrix.\r\nprint('The trace value of the given matrix is :', mtrxtrace)\r\n# Print the value of mtrxnormal which gives the value of the normal of the given matrix.\r\nprint('The normal value of the given matrix is :', mtrxnormal)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some random number of rows of the matrix = 4\r\nEnter some random number of columns of the matrix = 4\r\nEnter {4} elements of row {1} separated by spaces = 1 2 3 4\r\nEnter {4} elements of row {2} separated by spaces = 7 5 8 6\r\nEnter {4} elements of row {3} separated by spaces = 9 4 2 5\r\nEnter {4} elements of row {4} separated by spaces = 1 1 1 1\r\nThe trace value of the given matrix is : 9\r\nThe normal value of the given matrix is : 7.745966692414834<\/pre>\n<p>Dive into numerous <a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Python Programming Language Examples<\/a> for practice and get the best out of the tutorial and learn python one step at a time.<\/p>\n<ul>\n<li><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><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-the-sum-of-a-lower-triangular-matrix\/\">Python Program to Find the Sum of a Lower Triangular Matrix<\/a><\/li>\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<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In the previous article, we have discussed Python Program to Print Odd Numbers in Given Range Using Recursion Given a matrix and the task is to find the normal and trace of the given Matrix in Python. What is a matrix: A matrix is a rectangular sequence of numbers divided into columns and rows. A &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-to-find-the-normal-and-trace-of-a-matrix\/\"> <span class=\"screen-reader-text\">Python Program to find the Normal and Trace of a Matrix<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":20297,"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 Normal and Trace of a 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-normal-and-trace-of-a-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 Normal and Trace of a Matrix - Python Programs\" \/>\n<meta property=\"og:description\" content=\"In the previous article, we have discussed Python Program to Print Odd Numbers in Given Range Using Recursion Given a matrix and the task is to find the normal and trace of the given Matrix in Python. 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What is a matrix: A matrix is a rectangular sequence of numbers divided into columns and rows. 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