Laplace Expansion

Open access

Laplace Expansion

In the article the formula for Laplace expansion is proved.

[1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.

[2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

[4] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.

[5] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.

[6] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

[7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

[8] Czesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.

[9] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[10] Czesław Byliński. Semigroup operations on finite subsets. Formalized Mathematics, 1(4):651-656, 1990.

[11] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

[12] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

[13] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.

[14] Katarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711-717, 1991.

[15] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.

[16] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.

[17] Yatsuka Nakamura. Determinant of some matrices of field elements. Formalized Mathematics, 14(1):1-5, 2006.

[18] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.

[22] Andrzej Trybulec. Semilattice operations on finite subsets. Formalized Mathematics, 1(2):369-376, 1990.

[23] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.

[24] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1(1):187-190, 1990.

[25] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1(5):979-981, 1990.

[26] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.

[27] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.

[28] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.

[29] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[30] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

[31] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

[32] Xiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005.

[33] Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992.

[34] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993.

[19] Karol Pak. Basic properties of determinants of square matrices over a field. Formalized Mathematics, 15(1):17-25, 2007.

[20] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.

[21] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.

Formalized Mathematics

(a computer assisted approach)

Journal Information

SCImago Journal Rank (SJR) 2017: 0.119
Source Normalized Impact per Paper (SNIP) 2017: 0.237



Target Group

researchers in the fields of formal methods and computer-checked mathematics

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 79 79 17
PDF Downloads 20 20 6