Search
- https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.02%3A_Algebra_Support/1.2.01%3A_Real_Numbers_Linear_Inequalities_and_Interval_NotationThe vertical line | inside the braces reads, “such that” and the symbol ∈ indicates set membership and reads, “is an element of.” The notation above in its entirety reads, “the set of all number...The vertical line | inside the braces reads, “such that” and the symbol ∈ indicates set membership and reads, “is an element of.” The notation above in its entirety reads, “the set of all numbers ab such that a and b are elements of the set of integers and b is not equal to zero.” Decimals that terminate or repeat are rational.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_Theory/6.09%3A_Special_Factorizations/6.9E%3A_Exercises_for_Section_6.9This page offers exercises on Cholesky factorization, orthonormal bases, and positive definite matrices, including finding Cholesky factorizations and solving systems of equations. Techniques such as ...This page offers exercises on Cholesky factorization, orthonormal bases, and positive definite matrices, including finding Cholesky factorizations and solving systems of equations. Techniques such as Gram-Schmidt and QR factorization are used to establish orthonormal bases. The content also involves proving matrix operations that yield positive definite matrices, highlighting conditions for invertibility and scalar multiplication, ultimately providing practice problems in linear algebra.
- https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/02%3A_Algebra_Support/2.01%3A_Real_Numbers_Linear_Inequalities_and_Interval_NotationThe vertical line | inside the braces reads, “such that” and the symbol ∈ indicates set membership and reads, “is an element of.” The notation above in its entirety reads, “the set of all number...The vertical line | inside the braces reads, “such that” and the symbol ∈ indicates set membership and reads, “is an element of.” The notation above in its entirety reads, “the set of all numbers ab such that a and b are elements of the set of integers and b is not equal to zero.” Decimals that terminate or repeat are rational.
- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/03%3A_Exponents_Roots_and_Factorization_of_Whole_Numbers/3.05%3A_The_Least_Common_MultipleFor the GCF, we attach the smallest exponents to the common bases, whereas for the LCM, we attach the largest exponents to the bases. \(\begin{array} {ccll} {90} & = & {2 \cdot 45 = 2 \cdot 3 \cdot 15...For the GCF, we attach the smallest exponents to the common bases, whereas for the LCM, we attach the largest exponents to the bases. 90=2⋅45=2⋅3⋅15=2⋅3⋅3⋅5=2⋅32⋅5630=2⋅315=2⋅3⋅105=2⋅3⋅3⋅35=2⋅3⋅3⋅5⋅7 =2⋅32⋅5⋅7
- https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Rings_with_Inquiry_(Janssen_and_Lindsey)/01%3A_The_Integers/1.03%3A_Primes_and_FactorizationAs described in the Introduction, our main goal is to build a deep structural understanding of the notion of factorization.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/02%3A_Matrices/2.04%3A_LU_FactorizationAn LU factorization of a matrix involves writing the given matrix as the product of a lower triangular matrix L which has the main diagonal consisting entirely of ones, and an upper triangular...An LU factorization of a matrix involves writing the given matrix as the product of a lower triangular matrix L which has the main diagonal consisting entirely of ones, and an upper triangular matrix U in the indicated order.
