Problem Composer
Matrix Algebra
Determinant, inverse, trace va rank auditlari uchun square matrix kiriting.
Preset
Vector Transform Primer
Experience
advanced
Matrix oilalari, transform va tensor lane'lar shu shell ichida ishlaydi.
Input Rules
- Rows `;` bilan ajratiladi.
- Bir qatordagi elementlar bo'sh joy yoki `,` bilan ajratiladi.
- Tensor slice'lari `||` bilan ajratiladi.
- Higher-order tensor bloklari `###` bilan ajratiladi.
- RHS vector optional, `systems`, `transform` va `tensor contraction` lane'da foydali.
Rendered Preview
2 1; 1 3
probe = 1; 0
Matrix Heatmap
Signed intensity of the active matrix coefficients
2x2
2
1
1
3
Pivot Structure
Pivot structure not reported for this lane.
Sparse Profile
Sparse density summary appears when a solver lane reports matrix sparsity.
Sparsity Pattern
Non-zero structure matrix zichligi va sparse-friendly zonalarni ko‘rsatadi.
Operation Trace
Elimination, factorization yoki transform oqimi
Trace preview analytic solve tayyor bo‘lganda shu yerda ko‘rinadi.
Singular Spectrum
Relative magnitude of singular values
Singular values appear when decomposition audit is available.
Residual / Stability
Residual norm: Not reported
Spectral radius: Not reported
Solver lane: Direct
Numerical Fallback
Analytic form unavailable
Analytic status: closed-form result topilmadi yoki symbolic lane javob bermadi.
Numerical lane: algebra rejimida matrix audit va struktur reading tayyor.
Quyidagi tugma orqali numerical interpretation step-by-step ko'rinadi.
Visualization Notes
Matrix heatmap
Det(A) = pending
Conditioning pending
Inverse unavailable or pending
Probe / RHS
1 ; 0
Final Result Synthesis
Determinant
pending
Trace
pending
Rank
2
Inverse
not ready
Condition
pending
Sparse
pending
Method Trace
Matrix lane auto-solve tayyor. Analytic form topilsa step-by-step shu yerda chiqadi; aks holda numerical fallback tugmasi shu blokni ochadi.
Phase: idle
Compute: starteralgebra