Recitation Notes Spring 16, 21-241: Matrices and Linear Transformations February 9, 2016
... 1. Let u, v be vectors in Rn . Note the difference between u · v and uT v even though they evaluate to the same ’value’. 2. Matrix addition is defined on matrices of the same size. 3. Matrix multiplication is defined when the number of columns of the first matrix is the same as the number of rows of ...
... 1. Let u, v be vectors in Rn . Note the difference between u · v and uT v even though they evaluate to the same ’value’. 2. Matrix addition is defined on matrices of the same size. 3. Matrix multiplication is defined when the number of columns of the first matrix is the same as the number of rows of ...
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... to conclude that E takes the form of a diagonal matrix whose diagonal entries are all the same element e ∈ S. Furthermore, this e is an idempotent. From this, it is easy to derive that e is in fact a multiplicative identity of S (multiply an element of the form U (a, 1, 1), where a is an arbitrary e ...
... to conclude that E takes the form of a diagonal matrix whose diagonal entries are all the same element e ∈ S. Furthermore, this e is an idempotent. From this, it is easy to derive that e is in fact a multiplicative identity of S (multiply an element of the form U (a, 1, 1), where a is an arbitrary e ...
MatLab - Systems of Differential Equations
... the nature of the equilibrium, and the eigenvalues and eigenvectors of the linearized system near the equilibrium. Another useful feature under the Solutions menu is to Show nullclines. The nullclines tell where trajectories are either horizontal or vertical. The intersection of two different color ...
... the nature of the equilibrium, and the eigenvalues and eigenvectors of the linearized system near the equilibrium. Another useful feature under the Solutions menu is to Show nullclines. The nullclines tell where trajectories are either horizontal or vertical. The intersection of two different color ...
Matrix algebra for beginners, Part II linear transformations
... · · · , bn form a basis set in a vector space if, and only if, each vector in the space can be represented uniquely as a sum of scalar multiples of the basis vectors, as in (2). There are two requirements here. The first is that you need enough basis vectors to represent every vector in the space. S ...
... · · · , bn form a basis set in a vector space if, and only if, each vector in the space can be represented uniquely as a sum of scalar multiples of the basis vectors, as in (2). There are two requirements here. The first is that you need enough basis vectors to represent every vector in the space. S ...
MATH 412: NOTE ON INFINITE-DIMENSIONAL VECTOR SPACES
... we choose the answer to be “yes”. 2. General definitions We now summarize what we saw in the examples above. For this let V be a vector space over a field F , and fix S ⊂ V . The proofs are all the same as in the finite-dimensional case and can also be found in my notes for Math 223 (see my website) ...
... we choose the answer to be “yes”. 2. General definitions We now summarize what we saw in the examples above. For this let V be a vector space over a field F , and fix S ⊂ V . The proofs are all the same as in the finite-dimensional case and can also be found in my notes for Math 223 (see my website) ...
