Let e80039b295b8568b88" title="Click to view the MathML source">m,n≥3, (m−1)(n−1)+2≤p≤mn, and u=mn−p. The set Ru×n×m of all real tensors with size 83" class="mathmlsrc">83.gif&_user=111111111&_pii=S0021869316303490&_rdoc=1&_issn=00218693&md5=413c97fefcf0ea759d339d90a27cf985" title="Click to view the MathML source">u×n×m is one to one corresponding to the set of bilinear maps a135fb0" title="Click to view the MathML source">Rm×Rn→Ru. We show that Rm×n×p has plural typical ranks p and p+1 if and only if there exists a nonsingular bilinear map a135fb0" title="Click to view the MathML source">Rm×Rn→Ru. We show that there is a dense open subset 8b65e1f46241c66b6bc5a13e438fac" title="Click to view the MathML source">O of Ru×n×m such that for any Y∈O, the ideal of maximal minors of a matrix defined by Y in a certain way is a prime ideal and the real radical of that is the irrelevant maximal ideal if that is not a real prime ideal. Further, we show that there is a dense open subset T of 8b4002952b3d3668b884ca4e48167" title="Click to view the MathML source">Rn×p×m and continuous surjective open maps 87345635826f14262b" title="Click to view the MathML source">ν:O→Ru×p and a116d748ca7bdb" title="Click to view the MathML source">σ:T→Ru×p, where Ru×p is the set of u×p matrices with entries in a1b766c83" title="Click to view the MathML source">R, such that if e587b25ca5" title="Click to view the MathML source">ν(Y)=σ(T), then if and only if the ideal of maximal minors of the matrix defined by Y is a real prime ideal.