Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1923. / Vita. Includes bibliographical references (p. 47).

Thesis (Ph. D.)--University of Michigan, 1929. / "Reprinted from the Transactions of the American mathematical society, vol. 34, no. 1."

Let U denote a finite dimensional vector space over an algebraically closed field F . In this thesis, we are concerned with rank one preservers on the r(th) symmetric product spaces r/VU and rank k preservers on the 2nd Grassmann product spaces 2/AU. The main results are as follows: (i) Let T : [formula omitted] be a rank one preserver. (a) If dim U ≥ r + 1 , then T is induced by a non-singular linear transformation on U . (This was proved by L.J. Cummings in his Ph.D. Thesis under the assumption that dim U > r + 1 and the characteristic of F is zero or greater than r .) (b) If 2 < dim U < r + 1 and the characteristic of F is zero or greater than r, then either T is induced by a non-singular linear transformation on U or [formula omitted] for some two dimensional sub-space W of U. (ii) Let [formula omitted] be a rank one preserver where r < s. If dim U ≥ s + 1 and the characteristic of F is zero or greater than s/r, then T is induced by s - r non-zero vectors of U and a non-singular linear transformation on U. (iii) Let T : [formula omitted] be a rank k preserver and char F ≠ 2. If T is non-singular or dim U = 2k or k = 2 , then T is a compound, except when dim U = 4 , in which case T may be the composite of a compound and a linear transformation induced by a correlation of the two dimensional subspaces of U. / Science, Faculty of / Mathematics, Department of / Graduate

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

Thesis (M. Phil.)--University of Hong Kong, 1973. / Typewritten.

Thesis (Ph. D.)--University of Missouri, 1931. / Vita. "Photo-lithoprint reproduction of author's manuscript." "Presented to the American mathematical society December 31, 1929." Includes bibliographical references (p. 20-21).

Thesis (Ph. D.)--University of Missouri, 1931. / Vita. "Photo-lithoprint reproduction of author's manuscript." "Presented to the American mathematical society December 31, 1929." Includes bibliographical references (p. 20-21).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1985. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 148-153).

Let U⊗V be a tensor product space over an algebraically closed field F ; let dim U = m and dim V = n ; let T be a linear transformation on U⊗V such that T preserves rank two tensors. We show that T preserves rank one tensors and this enables us to characterize T for all values of m and n. / Science, Faculty of / Mathematics, Department of / Graduate