Identity Matrix Calculator

Work out identity matrix instantly with clear inputs, formula shown and shareable results.

About Identity Matrix Calculator

The identity matrix has ones on the diagonal and zeros elsewhere, and leaves every vector unchanged. Scaling it by k gives a uniform dilation with determinant kⁿ and trace nk.

Formula

Identity

Iᵢⱼ = 1 if i = j, otherwise 0; AI = IA = A

Worked example

With the default values below, Identity Matrix Calculator returns Scaled identity matrix of [1, 0, 0, 0] [0, 1, 0, 0] [0, 0, 1, 0] [0, 0, 0, 1]. Change any input above and every figure here is recalculated in your browser.

Inputs used

Size naccepts 1–12: 4
Scale the identity by: 1

Results

Scaled identity matrix: [1, 0, 0, 0] [0, 1, 0, 0] [0, 0, 1, 0] [0, 0, 0, 1]
Determinant kⁿ: 1.000000
Trace nk: 4.000000
Non-zero entries: 4

Step by step

1Values used
2Identity
3Scaled identity matrix= [1, 0, 0, 0] [0, 1, 0, 0] [0, 0, 1, 0] [0, 0, 0, 1]
4Determinant kⁿ= 1.000000
5Trace nk= 4.000000
6Non-zero entries= 4

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is the determinant of the 4 × 4 identity?

1, and scaling it by k gives k⁴.

Why does it matter?

It is the multiplicative identity for matrices, which is what makes the notion of an inverse meaningful.