Chapter 4
... to a mole of a substance. 10.1.3 – I can distinguish between the atomic mass of an element and its molar mass. 10.1.4 – I can describe how the mass of a mole of a compound is calculated. ...
... to a mole of a substance. 10.1.3 – I can distinguish between the atomic mass of an element and its molar mass. 10.1.4 – I can describe how the mass of a mole of a compound is calculated. ...
Lecture notes
... group. We claim that O(n) has a natural manifold structure. Let us apply Theorem 2.1. Notice that a single matrix equation such as AAT = E is in fact a system of n2 equations for the n2 matrix entries. Obviously it cannot be independent, otherwise it would specify a single point (at best). To see th ...
... group. We claim that O(n) has a natural manifold structure. Let us apply Theorem 2.1. Notice that a single matrix equation such as AAT = E is in fact a system of n2 equations for the n2 matrix entries. Obviously it cannot be independent, otherwise it would specify a single point (at best). To see th ...
On the topological boundary of the one
... σ(T ) = {λ ∈ C : T − λ is not invertible}, σl (T ) = {λ ∈ C : T − λ is not left invertible}, σπ (T ) = {λ ∈ C : T − λ is not bounded below}. It is well-known that ∂σ(T ) ⊂ σπ (T ) ⊂ σl (T ) ⊂ σ(T ). This implies in particular that the outer topological boundaries (= the boundaries of the polynomiall ...
... σ(T ) = {λ ∈ C : T − λ is not invertible}, σl (T ) = {λ ∈ C : T − λ is not left invertible}, σπ (T ) = {λ ∈ C : T − λ is not bounded below}. It is well-known that ∂σ(T ) ⊂ σπ (T ) ⊂ σl (T ) ⊂ σ(T ). This implies in particular that the outer topological boundaries (= the boundaries of the polynomiall ...