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- [Finite-Dimensional Linear Algebra] 2.2 Vector Spaces + 2.3 Subspaces The elements of vector space V are called vectors, and the elements of the corresponding field F are called scalars. Definition of a Vector SpaceLet F be a field and let V be a nonempty set with two operations defined with respect to these sets: (vector) addition: u,v∈V⇒u+v∈Vscalar multiplication: α∈F,v∈V⇒αv∈V V is a vecto.. Show More
- [Finite-Dimensional Linear Algebra] 4.1 + 4.2 + 4.3 The Determinant Function Analysis of matrices is central in the study of finite-dimensional linear algebra, because any linear operator mapping one finite-dimensional space into another can be represented by a matrix. The simplest kind of matrix ia a diagonal matrix. The matrix A∈Fm×n is diagonal if Aij=0 for all i≠j To simplify matrix-based calculations, we want to transform matrices into .. Show More
- [Finite-Dimensional Linear Algebra] 2.5 + 2.6 + 2.7 Basis and Dimension Lemma For a set of vectors u1,u2,…,un in vector space V, if v∈sp{u1,u2,…un}, thensp{u1,u2,…un,v}=sp{u1,u2,…un}This leads to the concept of a basis, a spanning set containing the fewest possible elements. Definition of a BasisLet u1,u2,…un be vectors in a vector space V. We say that {u1,u2,…un} is.. Show More
- [MIPS] MIPS Registers & Instructions RegistersNameNumberDescription$zero, $00contains the value 0$at1reserved for assembler$v0 - $v12-3values returned by functions$a0 - $a34-7arguments to functions$t0 - $t78-15temporary variables $s0 - $s716-23saved values $t8 - $t924-25more temporary registers$sp29stack pointer to the top of stack$ra31return addressTemporary vs. Saved RegistersMIPS convention specifies how the registers are suppo.. Show More