Biomech-Matrices Vectors Moments-Lecture

Biomech-Matrices Vectors Moments-Lecture - Matrices Vectors...

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Unformatted text preview: Matrices, Vectors, and Moments Introduction to Biomaterials 14:125:208 Matrices • You can multiply two matrices if the number of columns in the first matrix equals the number of rows in the second matrix. If not, it is undefined – The product matrix's dimensions are (rows of first matrix) × (columns of the second matrix ) Matrices Matrices Consider the following 4 5 4 2 4 1 3 1 7 1 1 2 2 1 2 1 1 2 2 1 4 1 1 2 2 2 1 1 1 2 1 2 2 2 1 1 2 1 1 1 1 2 1 1 2 1 2 1 2 1 BA AB B A Similarly Matrices • The transpose of a matrix consists of switching the rows and columns • Thus if – A=a ij – A T =a ji • A symmetric matrix – Where A=A T Matrices • A special symmetric matrix is the identity matrix • It can also be shown that – AI = A = IA Matrices • The Determinant – 2x2 matrix – The determinant of – Is – and is written as Matrices • Examples – Find the determinants Matrices • Determinant of a 3x3 matrix – Can be applied to this course – The determinant is – and is written as Matrices • Example – By definition – Where – So the determinant is: Matrices • Inverse matrix – The inverse of matrix A is A-1 – Where A A-1 = 1 – For = ? ? ? ? and −1 = 1 ¡ ? ¢? ¢? ? – −1 = 1 £¤−¥¦ ? ¢? ¢? ? Matrices • For A= ? 11 ? 12 ? 13 ? 21 ? 22 ? 23 ? 31 ? 32 ? 33 • −1 = 1 ¡ Matrices • So how can we use matrices in biomechanics?...
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This document was uploaded on 11/04/2011 for the course BIOCHEMIST 208 at Rutgers.

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Biomech-Matrices Vectors Moments-Lecture - Matrices Vectors...

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