About Eigenvalue and Eigenvector Calculator for PCA
This calculator finds the eigenvalues and eigenvectors of the covariance matrix of your columns, using the Jacobi rotation method, which is what principal component analysis needs. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The covariance matrix is symmetric, so its eigenvalues are real, and its eigenvectors are perpendicular to one another. The Jacobi method repeatedly rotates the matrix to remove its off-diagonal entries one pair at a time until it is diagonal; the diagonal then holds the eigenvalues and the accumulated rotations hold the eigenvectors.
It opens on three made-up marks columns. Maths and physics rise and fall together, while art moves the other way, so one component captures a "science versus art" contrast.
How to use Eigenvalue and Eigenvector Calculator for PCA
- Pick a sample dataset, or paste your own CSV with a header row and at least two numeric columns.
- Decide on standardising. Turn it on when the columns are in different units, off when they share one.
- Read the variance explained by PC1 and the scree chart to see how many components matter.
- Choose which two components to plot, if you have more than two, and look at the projection.
- Open the covariance matrix, eigenvector and loading tables to see how each variable contributes to each component.
- Copy the component scores to use in a spreadsheet or another tool.
Features
- Covariance matrix, or correlation matrix when columns are standardised.
- Eigenvalues and eigenvectors by the Jacobi rotation method, sorted from largest to smallest.
- Explained and cumulative variance as a chart and a table.
- A projection scatter on any two components, coloured by a text column when one is present.
- Eigenvector and loading tables, with a stable sign convention.
- Component scores for every row, copyable as tab-separated text.
- Up to 5,000 rows and 30 numeric columns, with iris, a two-variable example and a marks table built in.
Worked examples
Marks in maths, physics and art for 12 students gives eigenvalues 675.5, 45.41, 4.81
PC1 explains 93.1%; eigenvector (0.708, 0.644, -0.292).
Privacy: how it works
- Your table is parsed and analysed in your browser tab. Nothing is sent to Ulkaa or anyone else.
Tips
- A common rule of thumb is to keep enough components to explain 90 to 95% of the variance. The note under the result card tells you how many that is.
- Look for an elbow in the scree chart: components after it add little.
- Large loadings of the same sign mean the variables move together on that component; opposite signs mean a contrast between them.
- Remove ID columns and anything that is not a measurement before running PCA.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your table are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your table are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What is the Jacobi eigenvalue method?
An iterative algorithm for symmetric matrices that applies plane rotations to zero out off-diagonal entries until the matrix is diagonal.
Are eigenvectors unique?
Only up to sign (and up to rotation when two eigenvalues are equal). This tool fixes the sign so the largest entry is positive.
More PCA Visualizer pages
- PCA VisualizerPaste numeric columns and see the covariance matrix, eigenvectors, explained variance and a 2D projection.
- PCA Covariance Matrix CalculatorSee the covariance matrix that PCA starts from, with its eigenvalues and eigenvector.
- PCA Explained Variance CalculatorSee how much variance each principal component explains, and how many you need.
- PCA With StandardizationRun PCA on standardised columns, so every variable has the same weight.
- PCA: PC2 vs PC3 PlotChoose any two components for the scatter, here the second and third.
- PCA on Two VariablesSee PCA at its simplest, with two variables and the correlation matrix.