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Lemonergy · Studio block

Gram matrix

Calculates the Gram matrix AᴴA, including complex conjugation.

Implementation ID
native-gram-matrix
Reviewed
2026-10-27

Behavior

Y = AᴴA; Yᵢⱼ = Σₖ conjugate(Aₖᵢ) Aₖⱼ. The worked example connects this operation to signals in Lemonergy Studio.

Interface

Gram matrix interfaceInputs or arguments on the left, observed outputs on the right. Conserving terminals appear below the component. The tables give units and behavior.Gram matrixStudio blockin0out0
Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.
Ports and observed outputs
NameDirectionUnitMeaning
in0input1A; real 2 × 2 array.
out0output1AᴴA; real 2 × 2 array.

Parameters

No configurable parameters for this component.

Equations and rules

  • Y = AᴴA; Yᵢⱼ = Σₖ conjugate(Aₖᵢ) Aₖⱼ

Worked example

Gram matrix — worked example

A = [1,3,2,4]. AᴴA at 0 s = [10,14,14,20].

Open Studio example after release →
Numerical checks for the bundled synthetic example
OutputTime (s)Expected valueUnitAbsolute tolerance
AᴴA
out0		0[10, 14, 14, 20]11e-08

Explore the recorded outputs

Gram matrix recorded example

Gram matrix [1, 1]
Gram matrix [1, 1] against timeRecorded synthetic simulation values. Time in seconds; output in —.9.509.750.25100.510.250.7510.51—Time (s)
Gram matrix [1, 1]: 10 — at 0 s

2 actual recorded samples. Lines are visual guides between samples. Synthetic example, not measured cell data.

Download the recorded samples (JSON) · Open this Studio example after release

Use in a workflow

Gram matrix — worked example

Calculates the Gram matrix AᴴA, including complex conjugation.

  1. Gram matrix: Y = AᴴA; Yᵢⱼ = Σₖ conjugate(Aₖᵢ) Aₖⱼ. The worked example connects this operation to signals in Lemonergy Studio.
    • Use the block reference for settings and connections.
    • Implementation tested locally; public release pending.
Open Studio example after release

Connected concepts

Limits and interpretation

  • Gram matrix A^H*A (conjugating complex first factor), not A*A.
  • Shapes and element types are explicit. Values must be finite; automatic reshaping and unit conversion are not performed.

Scientific and mathematical references

These sources explain the scientific and mathematical background. The behavior, interface and limits above define the Lemonergy implementation; a citation does not imply every model option in the source is implemented.

  1. NIST Digital Library of Mathematical Functions, §3.2 Linear Algebra

    National Institute of Standards and Technology

    Technical reference · Linear algebra and matrix operations; conceptual background, not software certification.

Implementation sources

This reference follows the public interface and locally verified numerical checks for an upcoming release.

Contract: Lemonergy Studio public contract · Verification record: verification-2026-10-27

  • docs/glossary/native-block-verification.json

This implementation and its workflow uses (JSON) · Knowledge graph (JSON-LD)