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called alternants# s last memoirs, %yl'ester(1)*@- and Cayleybean

their work#

&he study of special forms of determinants has been the natural result of the completion

of the eneral theory# s was the first# In

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the !orent" roup of special relati'ity and, more specifically, by their beha'ior under the spin

roup#

2.e. &inear com"inations of 'uantum states

Collision reactions such as occur in particle accelerators, where noninteractin particles

head towards each other and collide in a small interaction "one, with a new set of noninteractin

particles as the result, can be described as the scalar product of outoin particle states and a

linear combination of inoin particle states# &he linear combination is i'en by a matrix known

as the %matrix, which encodes all information about the possible interactions between particles#

2.f. (ormal modes

< eneral application of matrices in physics is to the description of linearly coupled

harmonic systems# &he e0uations of motion of such systems can be described in matrix form,

with a mass matrix multiplyin a enerali"ed 'elocity to i'e the kinetic term, and a force matrix

multiplyin a displacement 'ector to characteri"e the interactions#

2.#. !eometrical optics

7eometrical optics pro'ides further matrix applications# In this approximati'e theory,

the wa'e nature of liht is nelected# &he result is a model in which liht rays are indeed

eometrical rays#

2.f. )lectronics

&raditional mesh analysis in electronics leads to a system of linear e0uations that can bedescribed with a matrix#

3. %ample atrices $ro"lems

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C# ?ord Aroblem

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efferences5

http5www#shelo'esmath#comalebraad'ancedalebramatricesandsol'insystemswith

matrices

http5en#wikipedia#orwikiBatrixN(mathematics-

http5math#tutor'ista#comalebraapplicationofmatricesanddeterminants#html

http://www.shelovesmath.com/algebra/advanced-algebra/matrices-and-solving-systems-with-matrices/http://www.shelovesmath.com/algebra/advanced-algebra/matrices-and-solving-systems-with-matrices/http://en.wikipedia.org/wiki/Matrix_(mathematics)http://math.tutorvista.com/algebra/application-of-matrices-and-determinants.htmlhttp://en.wikipedia.org/wiki/Matrix_(mathematics)http://math.tutorvista.com/algebra/application-of-matrices-and-determinants.htmlhttp://www.shelovesmath.com/algebra/advanced-algebra/matrices-and-solving-systems-with-matrices/http://www.shelovesmath.com/algebra/advanced-algebra/matrices-and-solving-systems-with-matrices/