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In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. [1] [2]Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines, which break it up, or partition it, into a collection of smaller matrices.
The group 12 elements zinc, cadmium, and mercury are sometimes regarded as main group, rather than transition group, because they are chemically and physically more similar to the p-block elements than the other d-block elements. The group 3 elements are occasionally considered main group elements due to their similarities to the s-block ...
A partially balanced incomplete block design with n associate classes (PBIBD(n)) is a block design based on a v-set X with b blocks each of size k and with each element appearing in r blocks, such that there is an association scheme with n classes defined on X where, if elements x and y are ith associates, 1 ≤ i ≤ n, then they are together ...
[6] [7] The partition lattice of a 4-element set has 15 elements and is depicted in the Hasse diagram on the left. The meet and join of partitions α and ρ are defined as follows. The meet is the partition whose blocks are the intersections of a block of α and a block of ρ, except for
If A and B are sets and every element of A is also an element of B, then: . A is a subset of B, denoted by , or equivalently,; B is a superset of A, denoted by .; If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B which is not an element of A), then:
means that "x is an element of A". [1] Equivalent expressions are "x is a member of A", "x belongs to A", "x is in A" and "x lies in A". The expressions "A includes x" and "A contains x" are also used to mean set membership, although some authors use them to mean instead "x is a subset of A". [2]
A function (which in mathematics is generally defined as mapping the elements of one set A to elements of another B) is called "A onto B" (instead of "A to B" or "A into B") only if it is surjective; it may even be said that "f is onto" (i. e. surjective). Not translatable (without circumlocutions) to some languages other than English.
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.