Mathematical Calculators

## QR Decomposition Calculator

Find out orthonormal matrix and upper triangular matrix easily with our free online QR decomposition calculator!

## QR decomposition calculator

 ◦What is a QR decomposition? ◦How to calculate QR decomposition? ◦What is the Gram–Schmidt process? ◦How does Gram–Schmidt calculation work? ◦Does QR decomposition always exist? ◦Where QR factorization is used? ◦References
In linear algebra, factorizing a complex matrix makes it easier to analyze. QR decomposition is a matrix decomposition, which commonly used to solve linear systems, obtain eigenvalues, and calculations related to determinants. QR decomposition is also used in machine learning and on its applications.
Our QR decomposition calculator will calculate the upper triangular matrix and orthogonal matrix from the given matrix.
To use our calculator:
2. Insert matrix points
3. Choose rounding precision
4. See results
On this page, you will also learn how to calculate QR decomposition with Gram–Schmidt process, and where QR composition is used in real life.

## What is a QR decomposition?

QR decomposition is a technique used to convert a matrix into the form A = QR, where R equals upper triangular matrix, Q equals orthogonal matrix, and Q^(T)Q=I holds, where Q^(T) is the Qs' transpose, and I is the matrixs' identity.
QR decomposition is also known as QR factorization and QU factorization, and it is commonly used in solving equations linear systems.
Mathematical defition of QR decomposition

## How to calculate QR decomposition?

A QR decomposition can be performed through various methods. These include the Gram–Schmidt process, the Householder transformations, and the Givens rotations.
We will go through Gram–Schmidt process, and here is a step-by-step guide on how to calculate QR decomposition with it:
A = QR,
A = Given matrix
Q = Orthogonal matrix
R = Upper triangular matrix
1. Define matrix A
2. Take columns of A, and process them through Gram–Schmidt process. As of result, you get orthonormal vectors: e1, e2, ..., en.
3. Form a matrix Q with these vectors, by using vectors as columns.
4. Form matrix R by left-multiplying A with the transpose of Q (R = QᵀA)
There you go! You successfully calculate QR decomposition, and founded both orthogonal matrix and upper triangular matrix!
QR Decomposition with Gram-Schmidt method

## What is the Gram–Schmidt process?

The Gram-Schmidt process is a sequence of operations designed to transform a set of linearly independent vectors into an equivalent set of orthonormal vectors.

## How does Gram–Schmidt calculation work?

The Gram–Schmidt calculation is a mathematical tool used to determine the optimal fit between two sets of data. It’s often used in machine learning and data analysis, and it can be helpful when trying to find the best algorithms or models for predicting outcomes. In short, the Gram–Schmidt algorithm takes two sets of data—say, texts from a training set and predictions made from a model based on that data—and creates a similarity score between them. The higher the score, the more similar the sets are.
The Gram-Schmidt process is commonly used because it processes the calculations in an orthonormal base, which is often a much easier base to perform calculations.
Gram–Schmidt method

## Does QR decomposition always exist?

The factorization A = QR decomposition of a matrix A is a useful technique for estimating eigenvalues. It always exists when the rank of A is equal to the number of columns of A.

## Where QR factorization is used?

The concept of QR factorization is a very useful framework for various statistical and data analysis applications. One of these is the solution to the least square problems.
QR factorization is also a commonly used component in machine learning and its applications. It can be used for example to automatically remove an object from an image. Another example is extracting an image from a video clip.
QR factorization in data science

## References

Gander, W., 1980. Algorithms for the QR decomposition. Res. Rep, 80(02), pp.1251-1268.
Goodall, C.R., 1993. 13 Computation using the QR decomposition.
Article author
Angelica Miller
Angelica is a psychology student and a content writer. She loves nature and wathing documentaries and educational YouTube videos.
###### QR Decomposition Calculator English
Published: Thu Oct 07 2021
In category Mathematical calculators

#### Other mathematical calculators

Vector Cross Product Calculator

Vector cross product calculator finds the cross product of two vectors in a three-dimensional space.

30 60 90 Triangle Calculator

With our 30 60 90 triangle calculator you can solve the special right triangle.

Expected Value Calculator

This expected value calculator helps you to calculate an expected value (also called ​mean) of the given variable set with their probabilities.

Online Scientific Calculator

This scientific calculator provides simple and advanced mathematical functions in an easy-to-use app.

Standard Deviation Calculator

This free calculator gives you the standard deviation, variance, mean, and sum of a given data set.

Percentage Calculator

This percentage calculator is a free online calculator to calculate percentages. Find out what is X % of Y?

Fractions Calculator

This free fraction calculator can be used to find the result for adding, subtracting, multiplying, and dividing two common fractions.

Pounds To Cups Converter: Flour, Sugar, Milk..

Find out correct measurements for your favourite recipe with this free calculator converts pounds to cups easily! Works with US cups and UK cups!

Circle Circumference Calculator

Use this free circle circumference calculator to calculate circle radius, circle diameter, circle circumference, and circle area.

Double Angle Formula Calculator

Determine the double angle equivalent of a given angle with this free calculator! Find more information about the double angle formula.

Mathematical Root Calculator (square Root Calculator)

This free calculator calculates the second, third and higher exponents and roots. Formula is also available.

Triangle Area Calculator

Find out area of triangle easily with our free triangle area calculator! You can calculate with base and height, three different sides and many more. Works with angles and radians!

Coterminal Angle Calculator

Find out coterminal angles with our coterminal angle calculator! Works with degrees and radians to find out positive and negative coterminal angles!

Dot Product Calculator

Calculate mathematical dot products, scalar products and dot product angles easily for your vectors.

Midpoint Calculator

Find out midpoints for a line or a triangle easily with our midpoint calculator! This page will also teach you valuable midpoint formula!

Significant Figures Converter (Sig Figs Calculator)

Find out the correct amount of significant figures in your number easily with our significant figure tool!

Arc Length Calculator For Circle

Find out easily length of a circle's arc with this online math calculator!

Point Estimate Calculator

Calculate point estimate easily with our free online tool!

Percentage Increase Calculator

Calculate any percentage increase easily with our free online calculator!

Percentage Difference Calculator

Calculate percentage difference instantly with our mathematical percentage difference calculator!

Linear Interpolation Calculator

This free online calculator calculates the linear interpolation and the linear extrapolation. It also provides the slope of the linear equation.

Matrix Transpose Calculator

This matrix transpose calculator helps you to find a transpose for any matrix.

Triangle Hypotenuse Calculator

Find out hypotenuse for all kinds of triangles easily with our free math calculator!

Trigonometry Calculator

Calculate easily trigonometric values Sin, Cos, Tan, Cot, Sec and Csc with our free online calculator!

Right Triangle Side And Angle Calculator (triangle Calculator)

FInd out easily right side and angle of an triangle with our free online calculator!

45 45 90 Triangle Calculator (right Triangle Calculator)

Calculate hypotenuse, measurements and ratio easily with our 45 45 90 triangle calculator.

Matrix Multiply Calculator

Calculate matrix multiplications easily with our free online math calculator!

Average Calculator

Calculate mean average of numbers easily with our free online math calculator

Random Number Generator

This tool generates a truly random number between any two numbers.

Margin Of Error Calculator

This calculator calculates the margin of error for surveys based on sample size and proportion. It also allows you to set the desired level of confidence.

Angle Between Two Vectors Calculator

This online tool calculates the angle between two vectors and has all the possible vector combinations.

LCM Calculator - Least Common Multiple Calculator

This calculator will help you find the LCM or LCD for a particular set of numbers.

Square Footage Calculator

This online calculator calculates the area of a shape measured in feet. Works with all shapes and measurement units!

Exponent Calculator (power Calculator)

This is an online calculator that can calculate exponents.

Math Remainder Calculator

This online tool calculates the remainder of a division.

Rule Of Three Calculator - Direct Proportion

Calculate easily direct proportion of numbers with our free Rule of Three calculator.

Quadratic equations are any polynomial algebra of the second degree having the following form in algebra.

Sum Calculator

This summation notation calculator allows you to quickly calculate the summation of a set number, also known as Sigma. Therefore it is often called a sigma calculator. It also gives you a sample from the series to be a sum. It can be used in simple mode to calculate a simple sum using a given set of numbers.

Perimeter Calculator

This is a free online tool that will calculator the perimeter of different shapes.

Z Score Calculator (z Value)

This is a calculator that calculates the z-score of a data set.

Fibonacci Calculator

This Fibonacci calculator can be used to calculate the terms arbitrarily of the Fibonacci sequence.

Capsule Volume Calculator

It is a free calculator that can help you find the volume of any capsule.

Pyramid Volume Calculator

It is a free calculator that can help you find the volume of different shapes.

Triangular Prism Volume Calculator

It is a free calculator that can help you find the volume of any triangular prism.

Rectangle Volume Calculator

It is a free calculator that can help you find the volume of a box.

Cone Volume Calculator

This calculator calculates cone volume and can be used to solve school problems.

Cube Volume Calculator

This is an online tool that will calculate the volume of any cube.

Cylinder Volume Calculator

This is an online tool that will calculate the volume of a cylinder.

Scale Factor Dilation Calculator

This is an online calculator that will help you calculate the scale factor dilation of an object.

Shannon Diversity Index Calculator

The Shannon biodiversity index calculator can be used to calculate the diversity of species in a community. Ecologists can use the Shannon diversity index to gain useful information about habitat.

Bayes Theorem Calculator

Use this Bayes theorem calculator online to determine the probability of an event that is conditional on another. This calculation takes into account the prior probability of A, the probabilities B conditional and A conditional, and A conditional.

Antilogarithm Calculator

The antilog calculator allows you to calculate the inverse logarithm function. Calculate the antilogarithm for any number with any base, whether it's 10, natural antilog, or another number.

Eˣ Calculator

This amazing tool will allow you to compute e to the power of any number you choose.

Prime Number Calculator

This calculator will show you whether a number has a prime number or if it is a composite.

Exponential Growth Calculator

The exponential Growth Calculator calculates the final price of a quantity based on its initial values, rate of growth, and time.

Sample Size Calculator

Calculate sample size based on the population size, confidence level, and margin of error.

Inverse Logarithm (log) Calculator

This online calculator will display the inverse log of the number and the base entered.

Poisson Distribution Calculator

The Poisson distribution calculator will allow you to determine the likelihood of an event occurring a number of times during a certain time frame.

Multiplicative Inverse Calculator

This calculator will help you find the multiplicative inverse of an integer, a decimal, a fraction, or a mixed number.

Marks Percentage Calculator

This calculator converts test marks to percentages. It can be used to quickly calculate the percentage of one or more test grades (marks), and the maximum number of marks.

Ratio Calculator

This calculator can be used to determine the dimensions of images when you resize them.

Empirical Rule Calculator

The empirical rule calculator, also known as a "68 95 99 rule calculation", is a tool that allows you to determine the ranges that are either 1 or 2 standard deviations or 3 standard deviations. This calculator will show you the ranges in which 68, 95, or 99.7% of normally distributed data, respectively.

P-value-calculator

This incredible tool will allow you to find the p-value. You can use test statistics to determine which p-value is one-sided and which is two-sided.

Sphere Volume Calculator

It is a free calculator that can help you find the volume of a sphere.

NPV Calculator

This online calculator will allow you to calculate the NPV (Net Present Value) of an investment. The calculation is based on the initial investment and the discount rate. You can also calculate Internal Rates of Return (IRR), gross returns, and net cash flows.

Percentage Decrease

Use this calculator to find out how a percentage decrease by any amount will change the result. Simply enter the original value, the percentage decrease, and the new value to calculate the change.

Area Calculator

Our intuitive tool lets you choose from different shapes and calculates their area in the blink of an eye.

Probability Calculator

The probability calculator lets you explore the relationships of likelihood between two separate events. This allows you to get a better understanding of how events are related, and thereby makes predictions more accurate.

Fraction To Decimal Calculator

Use our fraction to decimal calculator to easily convert fractions to decimals and back again!

Factor Calculator

Find out the factors of any number with our factor calculator

Fraction To Mixed Number Calculator

Convert a fraction to a mixed number calculator using our simple tool