As Zehfuss himself admits, in his youth he showed more interest in languages and history than mathematics. At the age of fifteen, he entered the Polytechnic in Darmstadt, where he devoted himself to the study of mathematics, mechanics, physics and chemistry, encouraged by his teacher Strecker, but continued to attend classes in Latin, French as well as German history and literature.

... with difficult parts of the subject that are only accessible to the more advanced mathematicians.

The operation defined by the symbol $\otimes$ was first used by Johann Georg Zehfuss in 1858. It has since been called by various names, including the Zehfuss product, the Producttransformation, the conjunction, the tensor product, the direct product and the Kronecker product. In the end, the Kronecker product stuck as the name for the symbol and operation, $\otimes$.

The Kronecker product, named after German mathematician Leopold Kronecker, is very important in the areas of linear algebra and signal processing. In fact, the Kronecker product should be called the Zehfuss product because Johann Georg Zehfuss published a paper in 1858 which contained the well-known determinant conclusion, $| \bf{A} \otimes \bf{B} | = | \bf{A} |^{n} | \bf{B} |^{m}$ for square matrices $\bf{A}$ and $\bf{B}$ with order $m$ and $n$.

Some historians of mathematics have questioned the association of the ⊗ product with Kronecker's name on the grounds that there is no known evidence in the literature for Kronecker's priority in its discovery or use. Indeed, Sir Thomas Muir's authoritative history [3] calls $det (A \otimes B)$ the 'Zehfuss determinant' of A and B because the determinant identity

$| A \otimes B | = | A |^{n} | B |^{m}$

appears first in an 1858 paper of Johann Georg Zehfuss ("Über eine gewisse Determinante Ⓣ, Zeitschrift für Mathematik und Physik 3 (1858), 298-301"). Following Muir's lead, a few later authors have called A ⊗ B the 'Zehfuss matrix' of A and B, for example "D E Rutherford, On the Condition that two Zehfuss matrices be equal, Bull. Amer. Math. Soc. 39 (1933), 801-808", and "A C Aitken, The normal form of compound and induced matrices, Proc. London Math. Soc 38 (2) (1935), 354-376". However, a series of influential texts at and after the turn of the century permanently associated Kronecker's name with the ⊗ product, and this terminology is nearly universal today. For further discussion (including claims by others to independent discovery of the determinant result) and numerous references, see "H V Henderson, F Pukelsheim and S R Searle, On the history of the Kronecker product, Linear and Multilinear Algebra 14 (2) (1983), 113-120".

Our story begins with one Johann Georg Zehfuss (1832-1901) at the University of Heidelberg who, according to biographical notes by Poggendorf (1863, 1898), published papers on determinants until at least 1868 before moving to studies in astronomy. In particular, Zehfuss (1858) contains the determinant result

$| A \otimes B | = | A |^{b} | B |^{a}$

for square matrices A and B of order a and b, respectively. Zehfuss wrote in terms of determinants rather than matrices, following the then customary practice of employing the term 'determinant' both for what we now call a square matrix as well as for its determinant. ... Unfortunately, the Zehfuss (1858) determinant result seems to have been overlooked for more than fifty years, until its rediscovery by Muir (1911, reprinted in [3]) who claims it for Zehfuss and accordingly calls $| A \otimes B |$ the Zehfuss determinant of A and B. Others, notably Rutherford (1933), and Aitken (1935) and his student Ledermann (1936), following Muir's lead, have gone further and called A $\otimes$ B the Zehfuss matrix of A and B. Aitken's adoption of this name is of interest in light of Ledermann's later (1968) comment that Aitken "was particularly fond of stressing the claims of lesser known mathematicians of former times for discoveries erroneously attributed to their more famous contemporaries. Many of his historical references were gleaned from Sir Thomas Muir's monumental work on determinants, for which Aitken had a profound admiration."

... that magnetic forces which the heavenly bodies mutually exert cannot effect this delay, whereas the constant magnetic field in which the planets move can cause a change in precession which could lead to an explanation of the observation.