Advanced Logical Matrix Calculator

Build, compare, and transform boolean matrices with ease. View instant truth counts and structure insights. Save outputs confidently for study, modeling, and verification tasks.

Evaluate boolean matrices using AND, OR, XOR, implication, complement, transpose, and boolean product. Inspect truth density, relation properties, row counts, column counts, and exportable outputs in one place.

Configuration

Element-wise operations need equal dimensions. Boolean product needs Columns A = Rows B.

Matrix A

Enter binary values using the selectors below.

Matrix B

Matrix B is used for paired operations and boolean product.

Example Data Table

Example Matrix A Matrix B Operation Expected Insight
1 [[1,0,1],[0,1,0],[1,1,0]] [[0,1,1],[1,0,1],[0,1,0]] AND Highlights positions where both matrices contain true values.
2 [[1,0],[0,1],[1,1]] [[1,0,1],[0,1,0]] Boolean Product Builds a logical connectivity matrix using AND-OR composition.
3 [[1,0,0],[1,1,0],[0,1,1]] [[1,1,0],[0,1,1],[0,0,1]] Implication Shows where A logically implies B at each matching cell.

Formula Used

Element-wise logic:
AND: cij = aij ∧ bij
OR: cij = aij ∨ bij
XOR: cij = aij ⊕ bij
XNOR: cij = ¬(aij ⊕ bij)
NAND: cij = ¬(aij ∧ bij)
NOR: cij = ¬(aij ∨ bij)
Implication logic:
A → B: cij = ¬aij ∨ bij
B → A: cij = ¬bij ∨ aij
Unary operations:
NOT A: cij = 1 - aij
NOT B: cij = 1 - bij
Transpose: cij = aji or bji
Boolean matrix product:
cij = ⋁k (aik ∧ bkj)
This means each result cell becomes true when at least one matching path contains two true links.

How to Use This Calculator

  1. Select the required matrix operation from the configuration panel.
  2. Choose the row and column sizes for Matrix A and Matrix B.
  3. Enter 0 or 1 values into each matrix cell.
  4. Use identical dimensions for element-wise operations.
  5. Use Columns A equal to Rows B for boolean product.
  6. Click Calculate Logical Matrix to generate the result.
  7. Review the output matrix, truth density, graph, and relation properties.
  8. Use the CSV or PDF buttons to export the result.

FAQs

1. What is a logical matrix?

A logical matrix is a matrix made of binary values, usually 0 and 1. These values represent false and true conditions for relations, paths, states, or decisions.

2. What is the boolean product used for?

Boolean product is useful for relation composition, graph reachability, and adjacency analysis. It replaces arithmetic multiplication with AND and addition with OR.

3. Why do some operations require equal matrix sizes?

Element-wise operations compare matching cells directly. That means each cell in Matrix A needs a corresponding cell in Matrix B at the same row and column position.

4. What does implication mean in matrix logic?

Implication checks whether each entry in A logically leads to the matching entry in B. The only false case is when A is true and B is false.

5. What is truth density?

Truth density is the percentage of entries equal to 1 in the result matrix. It helps you estimate how strong, connected, or permissive the logical structure is.

6. Why does the calculator test symmetry and transitivity?

Those checks are useful when the result is a square relation matrix. They help identify whether the matrix behaves like a formal mathematical relation.

7. Can I use this for graph or adjacency analysis?

Yes. A logical matrix often represents graph connectivity. Boolean products and transitivity checks are especially helpful for path and reachability studies.

8. What do CSV and PDF exports include?

CSV export includes the operation summary and result matrix values. PDF export captures the full result section, including summary cards, matrix table, and graph.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.