Enter each block matrix and instantly multiply determinants. See block-wise outputs, formulas, and fast graphs. Save polished summaries for homework, validation, teaching, and revision.
Choose the number of visible blocks, set each block size, enter the matrix values, and compute the overall determinant.
For a block diagonal matrix
its determinant is the product of the determinants of each diagonal block:
Off-diagonal blocks are zero blocks, so they do not change the product rule. If any block has determinant 0, the whole matrix determinant becomes 0.
| Block | Size | Matrix | Determinant |
|---|---|---|---|
| Block 1 | 2 × 2 | [[2, 1], [3, 4]] | 5 |
| Block 2 | 1 × 1 | [[6]] | 6 |
| Block 3 | 2 × 2 | [[1, 2], [0, 5]] | 5 |
| Overall determinant = 5 × 6 × 5 | 150 | ||
It is a square matrix built from smaller square blocks along the main diagonal. Every block outside that diagonal is a zero block.
Because block diagonal structure separates the matrix into independent diagonal blocks. The total determinant equals the product of the determinant of each square block.
The overall determinant becomes zero immediately. A single singular block makes the full block diagonal matrix singular as well.
No. Each block only needs to be square. Different diagonal blocks may have different dimensions, such as 1 × 1, 2 × 2, or 4 × 4.
Yes. The calculator accepts decimal numbers, negative values, and zeros. That makes it useful for classroom work, checking solutions, and quick validation.
It is best for small and medium blocks. Splitting a matrix into blocks already saves effort, so block diagonal form is much faster to evaluate manually and digitally.
The chart compares each block determinant and the cumulative product after each block. It helps you see how individual blocks affect the total result.
The export tools save the visible block summary, determinant values, and final answer. They are helpful for notes, assignments, reports, or checking later.
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.