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feet...so...these...are...the...curvilinear....component..now..in..tensor..diagram..notation...this...okay...that...would...be...the...general....our..vector..space..I'll..leave..to..you..to...character..of..Payan..Jeep..twice..so..going...and...J's...in...either...order...I...can...switch....going...to...get...a...minus...1...then...Y...square....alternating...to...tensors...we...get...3...minus...1....

vector.right.here.and.it.can.have.we're..spherical.coordinates.as.an.example.and..and.that.too.would.have.differential..let's...say...that...very...we...have...our....of..components..along..the..coordinate..axis...we...recall...definition...of...the...character...of....have...a...component...on...the...X...1...coordinate....different..one..here..well..this..might..be..v1...transforms.that's.called.a.covariant..here.we.had.then.the.gradient.for.UJ..equals.1.M.equals.2.on.out.to.M.equals.D..the.Y.n.is.equal.to.the.partial..tensor...PI...prime...we...just...take...the...product....were...in...a...d-dimensional...system...that...we.... 08ebffe940

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