Basic functions on matrices

Octave commands:

# --------------------------------
# Copy/Paste into the octave window
#
  A=[
+2,+2,+2;
+3,+3,+3;
+4,+4,+4];
#
A_T = A'
#


# --------------------------------
# Copy/Paste into the octave window
#
  A=[
+2,+2,+2;
+3,+3,+3;
+4,+4,+4];
#
traceA = trace(A)
#


# --------------------------------
# Copy/Paste into the octave window
#
  A=[
+2,+5,+1;
+5,-6,-8;
+1,-8,+5];
#
sA = 100.*A
#


# --------------------------------
# Copy/Paste into the octave window 
#
  A=[
+2,+5,+1;
+5,-6,-8;
+1,-8,+5];
#
  B=[
+2,+5,+1;
+5,-6,-8;
+1,-8,+5];
#
AB = A*B
AplusB = A+B
AminsB = A-B
#


# --------------------------------
# Copy/Paste into the octave window 
#
  A=[
+2,+5,+1;
+5,-6,-8;
+1,-8,+5];
#
An = A^3
#


# -------------------------------- 
# Copy/Paste into the octave window
#
# A/B  = A*inv(B);
#
format short e;
#
  A=[
+2,+5,+1;
+5,-6,-8;
+1,-8,+5];
#
  B=[
+1,+1,+2;
+5,-3,-5;
+4,-8,+2];
#
AdivB = A/B
AinvB = A*inv(B)
#


# --------------------------------
# Copy/Paste into the octave window 
#
 A=[
+0.138,+0.626,+0.315,+0.818;
+0.800,+0.090,+0.658,+0.530;
+0.777,+0.488,+0.235,-0.150;
-0.552,+0.097,-0.728,-0.298]
#
 expm (A)
#


# --------------------------------
# Copy/Paste into the octave window 
#
 A=[
-9,-1,-1,+8,-9;
-7,-7,-1,+4,+8;
+6,+6,+4,-7,-5;
-7,-3,+6,-5,-3;
-9,-9,+8,-7,-7];
#
 det(A)
#
 
 
# --------------------------------
# Copy/Paste into the octave window 
#
 B=[
+2.00,-7.00,-5.00,-1.00;
+6.00,+4.00,-5.00,+6.00;
-3.00,-9.00,+4.00,+4.00;
-9.00,+4.00,+6.00,+4.00];
#
format short e;
#
 inv(B)
#
 

# --------------------------------
# Copy/Paste into the octave window 
#
 Ab=[
-325,-601,-801,-221,+360,+524;
-855,+832,+226,-815,-233,-143;
+724,-933,-49,-231,-965,-787;
+290,+238,-905,+772,-327,+446;
+636,-519,+662,-7,-375,-813];
#
format short e;
#
rref(Ab,.00000000001)
# 
 

# --------------------------------
# Copy/Paste into the octave window 
#
 a=[
+2,-9,-1;
+8,-1,-1;
-7,-7,+8;
-1,-7,-9;
+4,+2,+2];
#
format short e;
#
[Q, R] = qr (a,0) 
#
 
 
# --------------------------------
# Copy/Paste into the octave window 
#
 a=[
+22,+54,+14;
+54,-67,-83;
+14,-83,+52];
#
format short e;
#
EigenValues  = eigs (a,3) 
#

 
# --------------------------------
# Copy/Paste into the octave window  
#
 a=[
-3,+2,+8;
+2,+6,-3;
+8,-1,+2;
-1,-5,+2;
-7,+2,-1;
-9,+6,-1];
#
format short e;
#
SvdValue = svd (a,10)
# 
 

# --------------------------------
# Copy/Paste into the octave window 
#
 a=[
-367,+448;
+448,-847];
#
format short e
#
[V, E] = eigs (a,2) 
#
 

# --------------------------------
# Copy/Paste into the octave window 
#
 B=[
+4.00,-3.00,-9.00,+2.00;
-5.00,-7.00,-9.00,-3.00;
+8.00,+4.00,-7.00,-5.00;
+4.00,-5.00,+2.00,-7.00];
#
format short e
#
 [U, S, V] =svd (B,10)
# 
 

# --------------------------------
# Copy/Paste into the octave window 
#
 B=[
-3.00,+6.00,-9.00;
-3.00,-1.00,-1.00;
-9.00,-3.00,-3.00;
+6.00,-5.00,+6.00;
-3.00,-1.00,+6.00;
+8.00,-7.00,-9.00;
+2.00,-5.00,+2.00;
-1.00,+6.00,+6.00;
+8.00,-9.00,+4.00];
#
format short e
#
pinv(B)
#

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