Tensor: Difference between revisions

Revision as of 20:30, 17 June 2025

Revision as of 21:08, 17 June 2025

Line 223:

! rowspan=6 | ''n''

! scope="row" | 0

| [[Scalar (mathematics)|Scalarscalar]], e.g. [[scalar curvature]]

| [[Covectorcovector]], [[linear functional]], [[1-form]], e.g. [[multipole expansion|dipole moment]], [[gradient]] of a scalar field

| [[Bilinearbilinear form]], e.g. [[inner product]], [[quadrupole moment]], [[metric tensor]], [[Ricci curvature]], [[2-form]], [[symplectic form]]

| 3-form Ee.g. [[multipole moment|octupole moment]]

|

| Ee.g. ''M''-form i.e. [[volume form]]

|

|-

! scope="row" | 1

| [[Euclidean vector]]

| [[Linearlinear transformation]],<ref name="BambergSternberg1991">{{cite book|first1=Paul|last1=Bamberg|first2=Shlomo|last2=Sternberg|title=A Course in Mathematics for Students of Physics|volume=2|year=1991|publisher=Cambridge University Press|isbn=978-0-521-40650-5|page=669}}</ref> [[Kronecker delta]]

| Ee.g. [[cross product]] in three dimensions

| Ee.g. [[Riemann curvature tensor]]

|

|

Line 241:

|-

! scope="row" | 2

| Inverse [[metric tensor]], [[bivector]], e.g., [[Poisson structure]], inverse [[metric tensor]]

|

| Ee.g. [[elasticity tensor]]

|

|

Line 259:

|-

! scope="row" | ''N''

|[[Multivectormultivector]]

|

|