ๅปๆๅฐๅบไธ็ multilinear map ๆๆ ๅฝขๅผ็ tensor
้ไนๅฏไปฅๅฏซๆ ๏ผๆณจๆ ๅฏๆฅๅ ็บๅๆธ๏ผๆไปฅ่ทไธ้ขๆญฃๅฅฝ็ธๅใ
(consolidated) product
่ไพไพ่ชช
ๅฎ็พฉ็บ
ๆฎ้ tensor
ๆฎ้็ tensor ่จ่ๅฆ ๏ผๆฏไฝฟ็จๆ็ไพ่กจ็คบ ใ้็จ็ๆ ๆณๅฏไปฅ็ด่ฆบ็ๆณๅบ้ไบ่กจ็คบๆณๆณ่กจ็คบ็ไฝ็ฝฎ
- ็ถ ๆฏๆ้็ถญๅบฆ๏ผmanifold ็ไฝฟ็จๅ ดๆฏ้ๅธธๅฆๆญค๏ผๆ๏ผ่ฎๆๆ consolidated form ไธฆไธๆๆไปปไฝๅ้ก
- ไฝ็ถ ๆฏ็ก้็ถญๅบฆๆ๏ผๅฐฑๆๅๆงไธๆ็ซ็ๅฏ่ฝใ
Basis of tensor space
็จๆกไพไพ็ๆดๅฎนๆ็่งฃ๏ผๅ่จญๆ็ถญๅบฆ ็็ฉบ้ ๏ผๅฏไปฅๅ่จญๅฎๆๅ ฉๅ basis
ไนๅฐฑๆฏ่ชช
ๅฏไปฅ่ขซ่ฆ็บ
ๆๆฏ่ฆ็บ็ฉ้ฃ
ๅ ฉๅ่กจ็คบๆณ็่ฝๆๅซๅ reshape๏ผๅจ https://www.math3ma.com/blog/the-tensor-product-demystified ไธญๆๅพๅฅฝ็ๅ็คบๅ