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Determinant differences and maximal minors turn coordinate changes into controlled algebraic data. Cramer coordinates and the uniqueness of a right factor will later translate matching minor vectors into a linear map.
7 direct Cards + 2 reused prerequisites = 9 unique Cards. This count is a selected Card closure, not a source-declaration count.
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Direct references: SR406 — The family of maximal minors in increasing row order · SR411 — Right multiplication scales every maximal minor by one determinant · SR297 — A determinant difference bound in the sup operator norm · SR425 — Cramer’s rule for coordinates of a row · SR431 — A unique right factor from proportional oriented maximal minors · SR439 — Maximal minors scaled by the reference ball volume · SR328 — The satellite polynomial is linear in the maximal-minor vector
Reused prerequisites: SR264 — A seminorm with two-sided bounds against a reference norm · SR235 — A weighted determinant polynomial with satellites
Read selected Card prerequisites before their uses. Levels are recomputed from the selected reachability-preserving projection; omitted source helpers remain traceable in the source exploration.
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Collects the determinants of all square submatrices with all columns and an increasing selection of rows.
MathlibAnnex.Matrix.maximalMinors
Immediate Card prerequisites: None in this selected scope
Used by in this scope: The satellite polynomial is linear in the maximal-minor vector · Maximal minors scaled by the reference ball volume · Right multiplication scales every maximal minor by one determinant
Controls determinant variation by replacing one matrix row at a time.
MathlibAnnex.ContinuousLinearMap.abs_det_sub_le_max
Immediate Card prerequisites: None in this selected scope
Used by in this scope: None in this selected scope
Expresses a row in the basis of the rows of an invertible square matrix through row-replacement determinants.
MathlibAnnex.Matrix.det_smul_vecMul_nonsingInv_eq_updateRowDet
Immediate Card prerequisites: None in this selected scope
Used by in this scope: A unique right factor from proportional oriented maximal minors
Adds linear row-replacement contributions to a base determinant.
MathlibAnnex.Satellite.satellitePolynomial
Immediate Card prerequisites: None in this selected scope
Used by in this scope: The satellite polynomial is linear in the maximal-minor vector
Records a norm through a seminorm, two positive comparison constants and continuity on the original normed space.
MathlibAnnex.EquivalentSeminorm
Immediate Card prerequisites: None in this selected scope
Used by in this scope: Maximal minors scaled by the reference ball volume
Expresses the configuration polynomial as a linear pairing with maximal minors.
MathlibAnnex.PluckerSupport.pluckerPairing_satelliteCoefficients_maximalMinors
Immediate Card prerequisites: The family of maximal minors in increasing row order · A weighted determinant polynomial with satellites
Used by in this scope: None in this selected scope
Fixes the volume factor and increasing-row signs.
MathlibAnnex.Matrix.ballVolumeScaledMaximalMinors
Immediate Card prerequisites: The family of maximal minors in increasing row order · A seminorm with two-sided bounds against a reference norm
Used by in this scope: None in this selected scope
Recovers a square factor and its determinant from proportional determinants of every ordered row tuple.
MathlibAnnex.Matrix.existsUnique_factor_of_orientedMaximalMinorsProportional
Immediate Card prerequisites: Cramer’s rule for coordinates of a row
Used by in this scope: None in this selected scope
Turns a square right factor into a common scalar on the family of maximal minors.
MathlibAnnex.Matrix.maximalMinors_mul
Immediate Card prerequisites: The family of maximal minors in increasing row order
Used by in this scope: None in this selected scope