Free · Algebra and geometric relations

Diagonal Sum of a Square Matrix

Find the trace of a two, three or four row square matrix.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For the worked example, Trace (2 × 2) = 5.

tr(A)=Σᵢ Aᵢᵢ

Worked example

Enter these known values and leave the other values blank.

Matrix size
2
a==1==
2
b==2==
3
Trace (2 × 2)
5

Assumptions and limitations

  • Only diagonal entries contribute. Off-diagonal entries may be left empty.
  • Each entry must lie strictly between −1000 and 1000. Signed entries are allowed.

Common questions

How do I use this relation?

Choose the relevant mode and enter independent known quantities. Leave a missing value empty where the control permits an inverse.

What do the displayed numbers mean?

The result follows the stated mathematical model. All dimensions must use consistent units; available unit selectors handle conversions.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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