Qr Factorization Calculator

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The QR Factorization Calculator computes the Q and R matrices from an input matrix, verifies orthogonality, and determines the matrix’s determinant and rank with specified precision and format options.

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Use Our Qr Factorization Calculator

Step-by-Step Guide to Using the QR Factorization Calculator

The QR Factorization Calculator is a powerful tool designed to perform QR factorization on a given matrix. Follow the steps below to use the calculator effectively.

Step 1: Input Matrix Dimensions

Begin by specifying the dimensions of your matrix.

  • Number of Rows: Enter the number of rows in the matrix. This value must be between 2 and 5 inclusive.
  • Number of Columns: Enter the number of columns in the matrix. Similarly, this value must be between 2 and 5 inclusive.

Step 2: Specify Calculation Settings

Next, configure how you want the results to be displayed.

  • Decimal Precision: Choose the number of decimal places for the calculations. Options include 2, 4, or 6 decimal places.
  • Matrix Display Format: Select how the matrices should be displayed. You can choose between a decimal format or a fraction format.

Step 3: Perform the Calculation

With the input and settings specified, initiate the QR factorization calculation. The calculator will internally execute the following logical steps:

  • Calculate Q Matrix: The orthogonal matrix Q is computed based on the provided matrix dimensions.
  • Calculate R Matrix: The upper triangular matrix R is derived using the computed Q matrix.

Step 4: View Results

After the calculation, the following results will be presented:

  • Q Matrix (Orthogonal Matrix): This is the result of the orthogonalization process, formatted according to your precision preference.
  • R Matrix (Upper Triangular Matrix): The upper triangular matrix output, formatted as per your chosen decimal precision.
  • Orthogonality Check (QT * Q ≈ I): A verification step showing that the Q matrix multiplied by its transpose approximates the identity matrix, confirming its orthogonality.
  • Matrix Determinant: Displays the determinant of the matrix, calculated from the Q and R matrices.
  • Matrix Rank: Shows the rank of the matrix, computed using the R matrix. Note that this will be displayed as an integer.

Use these results for deeper insights and applications in your mathematical or scientific endeavors!