Skip to content
OneKitly
Sign up · Sign in

Jordan Normal Form Calculator (J, P and block structure)

Exact Jordan form of a 1×1 to 6×6 matrix: the blocks from the ranks of (A−λI)ᵏ, the transition matrix P built from generalized eigenvector chains, and A·P = P·J checked exactly. When the characteristic polynomial does not split over ℚ it says so instead of guessing.

Related tools

All Statistics & probability tools →
Normal Distribution CalculatorCompute normal probabilities P(X≤x), P(X>x), P(a≤X≤b) or find x for a percentile, from the mean and standard deviation.Point-Slope Form CalculatorWrite y − y1 = m(x − x1) from a point and slope or two points, with the other line forms.RREF Calculator (Reduced Row Echelon Form)Gauss-Jordan elimination up to 10×10 in exact rational arithmetic, with every row operation written out as R₂ ← R₂ − 2R₁ and the matrix redrawn after each one. Augmented mode classifies the system and gives the solution set.Slope-Intercept Form CalculatorReduce any line — from two points, a point and slope, or standard form — to y = mx + b.ANOVA Calculator (One-Way)Full one-way ANOVA table — SS, df, MS, F and p — plus η², ω² and Cohen's f, because a significant F on its own tells you nothing about how large the difference is. The equal-variance assumption is stated, not buried.Average Deviation Calculator (mean absolute deviation)The average absolute deviation from the mean AND from the median — the median is the point that minimises it, which is worth seeing. Every |x − centre| is listed, and the standard deviation sits beside it for contrast: squaring makes SD react hard to a single outlier while the average deviation barely moves. The outlier preset is built to show exactly that.Bayes Theorem CalculatorCompute the posterior probability P(A|B) with the probability tree, the natural-frequency restatement and the base-rate lesson that makes a 99 % accurate test right only 16.7 % of the time.Beta Distribution CalculatorCompute beta-distribution probabilities on [0,1] from shape parameters α and β via the regularized incomplete beta function.

Jordan Normal Form Calculator (J, P and block structure) is free to use as often as you like, directly from this page. It covers the blocks from the ranks of (A−λI)ᵏ, the transition matrix P built from generalized eigenvector chains, and A·P = P·J checked exactly. When the characteristic polynomial does not split over ℚ it says so instead of guessing — adjust any of them and the result follows immediately.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Jordan Normal Form Calculator (J, P and block structure)?

Exact Jordan form of a 1×1 to 6×6 matrix: the blocks from the ranks of (A−λI)ᵏ, the transition matrix P built from generalized eigenvector chains, and A·P = P·J checked exactly. When the characteristic polynomial does not split over ℚ it says so instead of guessing.

What does it take into account?

It factors in the blocks from the ranks of (A−λI)ᵏ, the transition matrix P built from generalized eigenvector chains, and A·P = P·J checked exactly. When the characteristic polynomial does not split over ℚ it says so instead of guessing. Change any of them and the output follows immediately.

When would I actually use this?

Summarising a dataset before drawing conclusions from it, checking whether a difference between two groups is real, and putting an interval around an estimate.

What is the most common mistake?

Reading a p-value as the probability that the hypothesis is wrong. It is the probability of seeing data at least this extreme if the null were true — a different statement, and a much weaker one.

How is Jordan Normal Form Calculator (J, P and block structure) different from Normal Distribution Calculator?

They sit next to each other but answer different questions: Normal Distribution Calculator is the one to open when you need it to compute normal probabilities P(X≤x), P(X>x), P(a≤X≤b) or find x for a percentile, from the mean and standard deviation. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Point-Slope Form Calculator is the closest one after this: Write y − y1 = m(x − x1) from a point and slope or two points, with the other line forms.

What else is worth having open alongside it?

RREF Calculator (Reduced Row Echelon Form) and Slope-Intercept Form Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Distributions and test statistics are computed from their standard definitions, not from a lookup table, so results carry more digits than a printed table would. The assumptions each test makes are stated with it.

Further reading

All guides →
ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.ExplainerMean, Median and Mode: What's the Difference?Mean, median and mode all describe the 'middle' of your data — but answer different questions. Here's what each means, with examples and when to use which.ExplainerGeometric vs Arithmetic Mean: Which to UseThe arithmetic mean adds and divides; the geometric mean multiplies and takes a root. Learn which fits growth rates, ratios, and averages.How-toHow to Calculate Standard Deviation (Step by Step)Standard deviation measures how spread out your data is. Here's the formula, a worked example, and the difference between population and sample.ExplainerProbability Basics, With ExamplesProbability measures how likely something is, from 0 to 1. Here's the basic idea, how to combine events with AND and OR, and the complement.