2x2 Minor Calculator

Actual2×2unsigneddeletedrow/columnminor,zero-basedindices0/1,finitebinary64.

Description

A matrix minor is the determinant remaining after deleting a selected row and column.

A matrix minor is the determinant remaining after deleting a selected row and column.^[1]

For a 2-by-2 matrix this tool returns the surviving entry with zero-based indices, without applying cofactor signs.

When to use 2x2 Minor Calculator

For a 2-by-2 matrix this tool returns the surviving entry with zero-based indices, without applying cofactor signs.

How to use 2x2 Minor Calculator and how it works

Prepare matrix, row index, column index, using the input definitions and matching units below.
Enter the required fields and run 2x2 Minor Calculator.
Read result.value using the units, signs and ordering explained below.
Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.

Input field	Meaning	Value type	Requirement
actualMatrix	Finite 2-by-2 matrix with row order retained.	array of array of number	Required; other constraints below
actualRowIndex	Zero-based deleted row, integer 0 or 1.	number	Required; integer 0–1; finite; other constraints below
actualColumnIndex	Zero-based deleted column, integer 0 or 1.	number	Required; integer 0–1; finite; other constraints below

Require exactly a 2-by-2 finite matrix and row/column indices each integer 0 or 1. Return the entry at the opposite row and column as the unsigned deletion minor. No (-1)^(row+column) cofactor sign is applied.

minor_ij=A_(1-i,1-j)

Apply the input ordering, units and branch conditions stated above.

Output field	Meaning	Value type
result	Object containing the calculated or selected fields below.	object
result.value	Unsigned surviving matrix entry after the selected row and column deletion.	number

json

{
  "input": {
    "actualMatrix": [
      [
        1,
        2
      ],
      [
        3,
        4
      ]
    ],
    "actualRowIndex": 0,
    "actualColumnIndex": 1
  },
  "output": {
    "result": {
      "value": 3
    }
  }
}

Limitations and assumptions

The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.

All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.

Alternative or Complementary methods

Use Resultant of Two Quadratics Calculator for a complementary operation: The resultant of two quadratics is the determinant of their degree-specific Sylvester matrix.

Use Quartic Discriminant Calculator for a complementary operation: A polynomial discriminant vanishes at repeated roots and depends on a specified coefficient convention.

References

2x2 Minor Calculator — tool.io

Similar or alternative tools

Resultant of Two Quadratics Calculator
The resultant of two quadratics is the determinant of their degree-specific Sylvester matrix.
Quartic Discriminant Calculator
A polynomial discriminant vanishes at repeated roots and depends on a specified coefficient convention.