Matrix Quick Study Guide
... 1. Find each of the following (or mark them as incommensurate): M1+M1 M1+M2 M1+M3 M1+M4 M1+2M4 M1×M1 M1×M2 M1×M3 M2×M3 2. Write I4 (the 4x4 identity matrix). 3. Write a singular matrix that does not contain any 0’s. 4. Find two square matrices A and B that together show that matrix multiplication is ...
... 1. Find each of the following (or mark them as incommensurate): M1+M1 M1+M2 M1+M3 M1+M4 M1+2M4 M1×M1 M1×M2 M1×M3 M2×M3 2. Write I4 (the 4x4 identity matrix). 3. Write a singular matrix that does not contain any 0’s. 4. Find two square matrices A and B that together show that matrix multiplication is ...
On the q-exponential of matrix q-Lie algebras
... in the new context, since they virtually replace all additions for the ordinary case, especially for the so-called q-morphisms, or the q-exponentials. In the first article [2], we introduced the inversion operator τ, together with a general n × n q-determinant, with the purpose that our q-Lie groups ...
... in the new context, since they virtually replace all additions for the ordinary case, especially for the so-called q-morphisms, or the q-exponentials. In the first article [2], we introduced the inversion operator τ, together with a general n × n q-determinant, with the purpose that our q-Lie groups ...
Using Matrices to Perform Geometric Transformations
... Say you want to translate the figure 4 units to the left and 3 units up. You can do this by adding the translation matrix to the original matrix. The result is the final coordinates of the new figure. ...
... Say you want to translate the figure 4 units to the left and 3 units up. You can do this by adding the translation matrix to the original matrix. The result is the final coordinates of the new figure. ...
Chapter 3 – Group Theory – p. 1
... The product of two elements of the group is also an element of the group. 2. Identity element: The is an element E ∈ G , such that AE = EA = A for all A ∈ G . A ‘neutral’ element exists, which has no ‘effect’ on the other elements if the group. 3. Associative law: A( BC ) = ( AB )C for all A, B ,C ∈ ...
... The product of two elements of the group is also an element of the group. 2. Identity element: The is an element E ∈ G , such that AE = EA = A for all A ∈ G . A ‘neutral’ element exists, which has no ‘effect’ on the other elements if the group. 3. Associative law: A( BC ) = ( AB )C for all A, B ,C ∈ ...
Exam 1 solutions
... 7.(5pts) Ever striving for the perfect breakfast, you decide to mix Cracklin’ Oat Bran, glue, and toothpaste in your cereal bowl. I remind you that Cracklin’ Oat Bran contained 110 calories, 3 g of protein, 21 g of carbohydrates, and 3 g of fat per 28 g serving. Elmer’s glue contained 110 calories, ...
... 7.(5pts) Ever striving for the perfect breakfast, you decide to mix Cracklin’ Oat Bran, glue, and toothpaste in your cereal bowl. I remind you that Cracklin’ Oat Bran contained 110 calories, 3 g of protein, 21 g of carbohydrates, and 3 g of fat per 28 g serving. Elmer’s glue contained 110 calories, ...
Determinants of Block Matrices
... notice that, if also CD = DC, then (13) holds; but (13) does not mention D,1, and so the natural question to ask was whether (13) would hold even if D were not invertible (but still CD = DC). I eventually found a proof of this, when F is a eld, by using the principle of the irrelevance of algebraic ...
... notice that, if also CD = DC, then (13) holds; but (13) does not mention D,1, and so the natural question to ask was whether (13) would hold even if D were not invertible (but still CD = DC). I eventually found a proof of this, when F is a eld, by using the principle of the irrelevance of algebraic ...
Introduction to Matrices
... When multiplying two matrices, A and B, multiply the entries of the first row of matrix A and the first column of matrix B, then add those products up to make the first entry in matrix AB. ...
... When multiplying two matrices, A and B, multiply the entries of the first row of matrix A and the first column of matrix B, then add those products up to make the first entry in matrix AB. ...
