Are you asking about 𝑅𝑥(30)𝑅y(50)? Rx(30) is the rotation matrix around the x-axis with θ=30 Ry(50) is the rotation matrix around the y-axis with θ=50 . Both are 3x3 matrices with specific values for sin and cos of their respective angles. When you multiply these two matrices, you get a third matrix, which is provided on the slide. This resulting matrix is both unitary and special.
@@alanthayer8797 𝑅𝑥(30)𝑅y(50) is a 3x3 matrix and it is the product of the two 3x3 matrices presented. That 3x3 matrix has numbers in it and those numbers in decimal form are the numbers in the matrix 𝑅𝑥(30)𝑅y(50). I give that matrix the name O because it is an orthogonal matrix as it is a member of the group SO(3). In order to demonstrate that it is orthogonal one needs to show OOTranspose equals to the identity matrix and O is special so its determinant must be 1.
@@alanthayer8797 You were absolutely right about the excessive number of decimal places. I should have set the software to round the results to three decimal places for better clarity and educational value. I appreciate your keen observation and your helpful correction regarding the expression of values like sin(50) * cos(30). Your input is invaluable in improving the quality of the material.
At 10:27 u did NOT Explain how did u Derive & WHAT r all those numbers /degrees w/n da Bracket
Are you asking about 𝑅𝑥(30)𝑅y(50)? Rx(30) is the rotation matrix around the x-axis with θ=30 Ry(50) is the rotation matrix around the y-axis with θ=50 . Both are 3x3 matrices with specific values for sin and cos of their respective angles. When you multiply these two matrices, you get a third matrix, which is provided on the slide. This resulting matrix is both unitary and special.
Explain derivation ofda decimal numbers w/n da bracket of R(30),R(50) Or explain O & O trace bracket numbers
@@alanthayer8797 𝑅𝑥(30)𝑅y(50) is a 3x3 matrix and it is the product of the two 3x3 matrices presented. That 3x3 matrix has numbers in it and those numbers in decimal form are the numbers in the matrix 𝑅𝑥(30)𝑅y(50). I give that matrix the name O because it is an orthogonal matrix as it is a member of the group SO(3). In order to demonstrate that it is orthogonal one needs to show OOTranspose equals to the identity matrix and O is special so its determinant must be 1.
@@acephysics123 but What does 30deg & 50 deg have to do with 9 different place holders of 9 different decimals arranged?
@@alanthayer8797 You were absolutely right about the excessive number of decimal places. I should have set the software to round the results to three decimal places for better clarity and educational value. I appreciate your keen observation and your helpful correction regarding the expression of values like sin(50) * cos(30). Your input is invaluable in improving the quality of the material.