The invention claimed is:1. A magnetic recording medium comprising a recording layer, a nonmagnetic layer, a substrate and a back layer; wherein,an average thickness of the magnetic recording medium tT satisfies 3.5 μm≤tT≤5.5 μm,a dimensional change amount Δw in a width direction of the magnetic recording medium with respect to a tension change in a longitudinal direction of the magnetic recording medium satisfies 700 ppm/N≤Δw≤8000 ppm/N, andwherein the dimensional change amount Δw is determined according to:where D(0.2N) and D(1.0N) represent widths of a sample of the magnetic recording medium subject to loads of 0.2N and 1.0N, respectively, in the longitudinal direction.2. The magnetic recording medium according to claim 1, wherein the dimensional change amount Δw satisfies 750 ppm/N≤Δw≤8000 ppm/N.3. The magnetic recording medium according to claim 1, wherein the dimensional change amount Δw satisfies 800 ppm/N≤Δw≤8000 ppm/N.4. The magnetic recording medium according to claim 1, whereina temperature expansion coefficient α of the magnetic recording medium satisfies 6 ppm/° C.≤α≤8 ppm/° C., anda humidity expansion coefficient β of the magnetic recording medium satisfies β≤5 ppm/% RH.5. The magnetic recording medium according to claim 1, wherein a Poisson's ratio ρ of the magnetic recording medium satisfies 0.3≤ρ.6. The magnetic recording medium according to claim 1, wherein an elastic limit value σMD in the longitudinal direction of the magnetic recording medium satisfies 0.8N≤σMD, and wherein the elastic limit value σMD is determined by a sample of the magnetic recording medium at 0.5 mm/min to obtain a distance versus load relationship.7. The magnetic recording medium according to claim 6, wherein the elastic limit value σMD does not depend on a rate V in elastic limit measurement.8. The magnetic recording medium according to claim 1, wherein an arithmetic mean roughness Ra of a magnetic surface of the magnetic recording medium is 2.0 nm or less.9. The magnetic recording medium according to claim 1, further comprising a magnetic surface and a back surface on an opposite side to the magnetic surface,whereinan interlayer friction coefficient μ between the magnetic surface and the back surface satisfies 0.20≤μ≤0.80.10. The magnetic recording medium according to claim 1, wherein a plurality of inverted V-shaped servo patterns is recorded on the recording layer.11. The magnetic recording medium according to claim 1, wherein a squareness ratio in a perpendicular direction of the magnetic recording medium is 65% or more.12. The magnetic recording medium according to claim 1, wherein a squareness ratio in a perpendicular direction of the magnetic recording medium is 73% or more.13. The magnetic recording medium according to claim 1, wherein a squareness ratio in a perpendicular direction of the magnetic recording medium is 80% or more.14. The magnetic recording medium according to claim 1, wherein a ratio R (=Hc(50)/Hc(25)*100) between a coercive force Hc (50) measured in a perpendicular direction of the magnetic recording medium at 50° C. and a coercive force Hc (25) measured in the perpendicular direction of the magnetic recording medium at 50° C. is 95% or more.15. The magnetic recording medium according to claim 1, wherein a peak ratio X/Y of a main peak height X of a switching field distribution (SFD) curve measured in a perpendicular direction of the magnetic recording medium to a sub-peak height Y near the zero magnetic field of the switching field distribution (SFD) curve satisfies 3.0≤X/Y≤100.16. The magnetic recording medium according to claim 1, wherein the recording layer has an average thickness tm satisfying 35 nm≤tm≤90 nm.17. The magnetic recording medium according to claim 1, wherein the recording layer includes a magnetic powder.18. The magnetic recording medium according to claim 17, wherein the magnetic powder includes an ε iron oxide magnetic powder and an average maximum particle size D of the ε iron oxide magnetic powder is 8 nm or more and 22 nm or less.19. The magnetic recording medium according to claim 18, wherein a coercive force Hc in a perpendicular direction is 220 kA/m or more and 310 kA/m or less.20. The magnetic recording medium according to claim 17, wherein the magnetic powder includes a hexagonal ferrite magnetic powder and an average particle size of the hexagonal ferrite magnetic powder is 15 nm or more and 30 nm or less.21. The magnetic recording medium according to claim 20, wherein a coercive force Hc in a perpendicular direction is 170 kA/m or more and 270 kA/m or less.22. The magnetic recording medium according to claim 17, wherein the magnetic powder includes a cobalt ferrite magnetic powder and an average particle size of the cobalt ferrite magnetic powder is 25 nm or less.23. The magnetic recording medium according to claim 1, wherein an average thickness of the substrate is 2.6 μm or more and 5.0 μm or less.24. The magnetic recording medium according to claim 1, wherein the substrate comprises a polyester.25. The magnetic recording medium according to claim 1, wherein the substrate comprises one or both of a polyethylene terephthalate (PET) and a polyethylene naphthalate (PEN).26. The magnetic recording medium according to claim 1, wherein an average thickness of the nonmagnetic layer is 0.6 μm or more and 2.0 μm or less.27. The magnetic recording medium according to claim 1, wherein an average thickness to of the back layer satisfies tb≤0.6 μm.28. The magnetic recording medium according to claim 1, wherein a surface roughness Rb of the back layer satisfies Rb≤6.0 nm.29. The magnetic recording medium according to claim 1, whereina plurality of inverted V-shaped servo patterns is recorded on the recording layer;the recording layer includes a magnetic powder including a hexagonal ferrite magnetic powder and an average particle size of the hexagonal ferrite magnetic powder is 15 nm or more and 30 nm or less;a coercive force Hc in a perpendicular direction is 170 kA/m or more and 270 kA/m or less;an average thickness of the substrate is 2.6 μm or more and 5.0 μm or less;the substrate comprises one or both of a polyethylene terephthalate (PET) and a polyethylene naphthalate (PEN);an average thickness of the nonmagnetic layer is 0.6 μm or more and 2.0 μm or less; andan average thickness tb of the back layer satisfies tb≤0.6 μm.30. A magnetic recording cartridge comprising a magnetic recording medium, a reel and a cartridge case, whereinthe magnetic recording medium comprises a recording layer, a nonmagnetic layer, a substrate and a back layer,an average thickness of the magnetic recording medium tT satisfies 3.5 μm≤tT≤5.5 μm, anda dimensional change amount Δw in a width direction of the magnetic recording medium with respect to a tension change in a longitudinal direction of the magnetic recording medium satisfies 700 ppm/N≤Δw≤8000 ppm/N, andwherein the dimensional change amount Δw is determined according to:where D(0.2N) and D(1.0N) represent widths of a sample of the magnetic recording medium subject to loads of 0.2N and 1.0N, respectively, in the longitudinal direction.