The tensor terminology (see this page for more definitions)
operation  super & 
expansion (using Einstein convention) 
equivalent vector and matrix notation  

dot product 
e_{i} A^{i}  e_{0} A^{0} + e_{1} A^{1} 


dot product  A_{i}^{j}b^{i}  A_{0}^{j}b^{0} + A_{1}^{j}b^{1} 


dot product  A_{i}^{j}B_{k}^{i}  A_{0}^{j}B_{k}^{0} + A_{1}^{k}B_{k}^{2} 


metric tensor  ds²=g_{p g}du^{p}du^{p} 


cross product a×b 
ε_{ijk}a^{j}b^{k} 


gram matrix G_{ij}  v_{i}^{T} v_{j}  (v_{i}  v_{j}) 


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see also: 

Correspondence about this page  
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