equation 5.162 eq:rep-special-orthogonal
open in the book ·
parts/02-mathematical-methods/03-linear-algebra-representations.tex:5643
- connected by a declared semantic edge
Rests on
No declared or derived dependency edges point away from this node yet.
Supports
-
depends_on
definition 5.131
Isotropic Cartesian tensor
¶
-
depends_on
definition A.672
The octahedral rotation group
¶
-
depends_on
proposition A.673
Cubic tensors of rank four
¶
-
depends_on
theorem A.675
Three constants for a cubic crystal, two for an
isotropic solid
¶
- depends_on remark A.676 The third cubic constant is measured, and it is not small ¶
-
depends_on
theorem A.675
Three constants for a cubic crystal, two for an
isotropic solid
¶
-
depends_on
proposition A.673
Cubic tensors of rank four
¶
-
depends_on
lemma 5.132
Parity constraint
¶
-
depends_on
theorem 5.133
Isotropic Cartesian tensors of rank at most four
¶
-
depends_on
lemma A.742
Isotropic representation
¶
- depends_on corollary A.743 Two scalar functions instead of a tensor field ¶
- depends_on lemma A.747 The third-order structure functions ¶
- depends_on lemma A.744 Vanishing of the pressure–velocity correlation ¶
-
depends_on
lemma A.671
The three products are independent
¶
- depends_on proposition A.673 Cubic tensors of rank four ¶ ↺
-
depends_on
lemma 30.26
Isotropic Cartesian tensors of rank four
¶
- depends_on phenomenon 30.28 Hooke's law ¶
- depends_on remark A.677 The lower ranks, and why an isotropic solid is not piezoelectric ¶
- depends_on remark 30.27 Two results this chapter borrows from Part II ¶
- depends_on remark 13.7 What the classification is used for ¶
-
depends_on
lemma A.742
Isotropic representation
¶
-
depends_on
theorem 5.133
Isotropic Cartesian tensors of rank at most four
¶
-
depends_on
definition A.672
The octahedral rotation group
¶
- depends_on lemma 5.132 Parity constraint ¶ ↺
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
← | Isotropic Cartesian tensor | declared | parts/02-mathematical-methods/03-linear-algebra-representations.tex:5706 |
depends_on |
← | Parity constraint | declared | parts/02-mathematical-methods/03-linear-algebra-representations.tex:5714 |